Tamil Nadu Board of Secondary EducationHSC Science Class 12

# Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide chapter 10 - Ordinary Differential Equations [Latest edition]

#### Chapters ## Solutions for Chapter 10: Ordinary Differential Equations

Below listed, you can find solutions for Chapter 10 of Tamil Nadu Board of Secondary Education Tamil Nadu Board Samacheer Kalvi for Class 12th Mathematics Volume 1 and 2 Answers Guide.

Exercise 10.1Exercise 10.2Exercise 10.3Exercise 10.4Exercise 10.5Exercise 10.6Exercise 10.7Exercise 10.8Exercise 10.9
Exercise 10.1 [Page 148]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide Chapter 10 Ordinary Differential Equations Exercise 10.1 [Page 148]

Exercise 10.1 | Q 1. (i) | Page 148

For the following equations, determine its order, degree (if exists)

("d"y)/("d"x) + xy = cot x

Exercise 10.1 | Q 1. (ii) | Page 148

For the following equations, determine its order, degree (if exists)

(("d"^3y)/("d"x^3))^(2/3) - 3 ("d"^2y)/("d"x^2) + 5("d"y)/("d"x) + 4 = 0

Exercise 10.1 | Q 1. (iii) | Page 148

For the following equations, determine its order, degree (if exists)

(("d"^2y)/("d"x^2))^2 + (("d"y)/("d"x))^2 = x sin(("d"^2y)/("d"x^2))

Exercise 10.1 | Q 1. (iv) | Page 148

For the following equations, determine its order, degree (if exists)

sqrt(("d"y)/("d"x)) - 4 ("d"y)/("d"x) - 7x = 0

Exercise 10.1 | Q 1. (v) | Page 148

For the following equations, determine its order, degree (if exists)

y(("d"y)/("d"x)) = x/((("d"y)/("d"x)) + (("d"y)/("d"x))^3

Exercise 10.1 | Q 1. (vi) | Page 148

For the following equations, determine its order, degree (if exists)

x^2 ("d"^2y)/("d"x^2) + [1 + (("d"y)/("d"x))^2]^(1/2) = 0

Exercise 10.1 | Q 1. (vii) | Page 148

For the following equations, determine its order, degree (if exists)

(("d"^2y)/("d"x^2))^3 = sqrt(1 + (("d"y)/("d"x)))

Exercise 10.1 | Q 1. (viii) | Page 148

For the following equations, determine its order, degree (if exists)

("d"^2y)/("d"x^2) = xy + cos(("d"y)/("d"x))

Exercise 10.1 | Q 1. (ix) | Page 148

For the following equations, determine its order, degree (if exists)

("d"^2y)/("d"x^2) + 5 ("d"y)/("d"x) + int y "d"x = x^3

Exercise 10.1 | Q 1. (x) | Page 148

For the following equations, determine its order, degree (if exists)

x = "e"^(xy((dy)/(dx))

Exercise 10.2 [Pages 151 - 152]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide Chapter 10 Ordinary Differential Equations Exercise 10.2 [Pages 151 - 152]

Exercise 10.2 | Q 1. (i) | Page 151

Express the following physical statements in the form of differential equation.

Radium decays at a rate proportional to the amount Q present

Exercise 10.2 | Q 1. (ii) | Page 151

Express the following physical statements in the form of differential equation.

The population P of a city increases at a rate proportional to the product of population and to the difference between 5,00,000 and the population

Exercise 10.2 | Q 1. (iii) | Page 151

Express the following physical statements in the form of differential equation.

For a certain substance, the rate of change of vapor pressure P with respect to temperature T is proportional to the vapor pressure and inversely proportional to the square of the temperature

Exercise 10.2 | Q 1. (iv) | Page 152

Express the following physical statements in the form of differential equation.

A saving amount pays 8% interest per year compound continuously. In addition, the income from another investment is credited to the amount continuously at the rate of ₹ 400 per year.

Exercise 10.2 | Q 2 | Page 152

Assume that a spherical rain drop evaporates at a rate proportional to its surface area. Form a differential equation involving the rate of change of the radius of the rain drop

Exercise 10.3 [Page 154]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide Chapter 10 Ordinary Differential Equations Exercise 10.3 [Page 154]

Exercise 10.3 | Q 1. (i) | Page 154

Find the differential equation of the family of all non-vertical lines in a plane

Exercise 10.3 | Q 1. (ii) | Page 154

Find the differential equation of the family of all non-horizontal lines in a plane

Exercise 10.3 | Q 2 | Page 154

Form the differential equation of all straight lines touching the circle x2 + y2 = r2

Exercise 10.3 | Q 3 | Page 154

Find the differential equation of the family of circles passing through the origin and having their centres on the x-axis

Exercise 10.3 | Q 4 | Page 154

Find the differential equation of the family of all the parabolas with latus rectum 4a and whose axes are parallel to the x-axis

Exercise 10.3 | Q 5 | Page 154

Find the differential equation of the family of parabolas with vertex at (0, –1) and having axis along the y-axis

Exercise 10.3 | Q 6 | Page 154

Find the differential equations of the family of all the ellipses having foci on the y-axis and centre at the origin

Exercise 10.3 | Q 7 | Page 154

Find the differential equation corresponding to the family of curves represented by the equation y = Ae8x + Be 8x, where A and B are arbitrary constants

Exercise 10.3 | Q 8 | Page 154

Find the differential equation of the curve represented by xy = aex + be–x + x2

Exercise 10.4 [Pages 157 - 158]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide Chapter 10 Ordinary Differential Equations Exercise 10.4 [Pages 157 - 158]

Exercise 10.4 | Q 1. (i) | Page 157

Show the following expressions is a solution of the corresponding given differential equation.

y = 2x2 ; xy’ = 2y

Exercise 10.4 | Q 1. (ii) | Page 157

Show the following expressions is a solution of the corresponding given differential equation.

y = aex + be–x ; y'' – y = 0

Exercise 10.4 | Q 2. (i) | Page 157

Find the value of m so that the function y = emx solution of the given differential equation.

y’ + 2y = 0

Exercise 10.4 | Q 2. (ii) | Page 157

Find the value of m so that the function y = emx solution of the given differential equation.

y” – 5y’ + 6y = 0

Exercise 10.4 | Q 3 | Page 157

The Slope of the tangent to the curve at any point is the reciprocal of four times the ordinate at that point. The curve passes through (2, 5). Find the equation of the curve

Exercise 10.4 | Q 4 | Page 157

Show that y = e–x + mx + n is a solution of the differential equation "e"^x(("d"^2y)/("d"x^2)) - 1 = 0

Exercise 10.4 | Q 5 | Page 157

Show that y = "a"x + "b"/x ≠ 0 is a solution of the differential equation x2yn + xy’ – y = 0

Exercise 10.4 | Q 6 | Page 157

Show that y = ae–3x + b, where a and b are arbitrary constants, is a solution of the differential equation ("d"^2y)/("d"x^2)  + 3("d"y)/("d"x) = 0

Exercise 10.4 | Q 7 | Page 157

Show that the differential equation representing the family of curves y2 = 2"a"(x + "a"^(2/3)), where a is a postive parameter, is (y^2 - 2xy ("d"y)/("d"x))^3 = 8(y ("d"y)/("d"x))^5

Exercise 10.4 | Q 8 | Page 158

Show that y = a cos bx is a solution of the! differential equation ("d"^2y)/("d"x^2) + "b"^2y = 0

Exercise 10.5 [Pages 161 - 162]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide Chapter 10 Ordinary Differential Equations Exercise 10.5 [Pages 161 - 162]

Exercise 10.5 | Q 1 | Page 161

If F is the constant force generated by the motor of an automobile of mass M, its velocity V is given by "M""dv"/"dt" = F – kV, where k is a constant. Express V in terms of t given that V = 0 when t = 0

Exercise 10.5 | Q 2 | Page 161

The velocity v, of a parachute falling vertically satisfies the equation "v" (dv)/(dx) = "g"(1 - v^2/k^2) where g and k are constants. If v and are both initially zero, find v in terms of x

Exercise 10.5 | Q 3 | Page 161

Find the equation of the curve whose slope is (y - 1)/(x^2 + x) and which passes through the point (1, 0)

Exercise 10.5 | Q 4. (i) | Page 161

Solve the following differential equation:

("d"y)/("d"x) = sqrt((1 - y^2)/(1 - x^2)

Exercise 10.5 | Q 4. (ii) | Page 161

Solve the following differential equation:

y"d"x + (1 + x^2)tan^-1x  "d"y= 0

Exercise 10.5 | Q 4. (iii) | Page 161

Solve the following differential equation:

sin  ("d"y)/("d"x) = a, y(0) = 1

Exercise 10.5 | Q 4. (iv) | Page 161

Solve the following differential equation:

("d"y)/("d"x) = "e"^(x + y) - x^3"e"^y

Exercise 10.5 | Q 4. (v) | Page 162

Solve the following differential equation:

(ey + 1)cos x dx + ey sin x dy = 0

Exercise 10.5 | Q 4. (vi) | Page 162

Solve the following differential equation:

(ydx - xdy) cot (x/y) = ny2 dx

Exercise 10.5 | Q 4. (vii) | Page 162

Solve the following differential equation:

("d"y)/("d"x) - xsqrt(25 - x^2) = 0

Exercise 10.5 | Q 4. (viii) | Page 162

Solve the following differential equation:

x cos y dy = ex(x log x + 1) dx

Exercise 10.5 | Q 4. (ix) | Page 162

Solve the following differential equation:

tan y ("d"y)/("d"x) = cos(x + y) + cos(x - y)

Exercise 10.5 | Q 4. (x) | Page 162

Solve the following differential equation:

("d"y)/("d"x) = tan^2(x + y)

Exercise 10.6 [Pages 165 - 166]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide Chapter 10 Ordinary Differential Equations Exercise 10.6 [Pages 165 - 166]

Exercise 10.6 | Q 1 | Page 165

Solve the following differential equation:

[x + y cos(y/x)] "d"x = x cos(y/x) "d"y

Exercise 10.6 | Q 2 | Page 165

Solve the following differential equation:

(x^3 + y^3)"d"y - x^2 y"d"x = 0

Exercise 10.6 | Q 3 | Page 166

Solve the following differential equation:

y"e"^(x/y) "d"x = (x"e"^(x/y) + y) "d"y

Exercise 10.6 | Q 4 | Page 166

Solve the following differential equation:

2xy"d"x + (x^2 + 2y^2)"d"y = 0

Exercise 10.6 | Q 5 | Page 166

Solve the following differential equation:

(y^2 - 2xy) "d"x = (x^2 - 2xy) "d"y

Exercise 10.6 | Q 6 | Page 166

Solve the following differential equation:

x ("d"y)/("d"x) = y - xcos^2(y/x)

Exercise 10.6 | Q 7 | Page 166

Solve the following differential equation:

(1 + 3"e"^(y/x))"d"y + 3"e"^(y/x)(1 - y/x)"d"x = 0, given that y = 0 when x = 1

Exercise 10.6 | Q 8 | Page 166

Solve the following differential equation:

(x2 + y2) dy = xy dx. It is given that y (1) = y(x0) = e. Find the value of x0

Exercise 10.7 [Page 169]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide Chapter 10 Ordinary Differential Equations Exercise 10.7 [Page 169]

Exercise 10.7 | Q 1 | Page 169

Solve the following Linear differential equation:

cos x  ("d"y)/("d"x) + y sin x  = 1

Exercise 10.7 | Q 2 | Page 169

Solve the following Linear differential equation:

(1 - x^2) ("d"y)/("d"x) - xy = 1

Exercise 10.7 | Q 3 | Page 169

Solve the following Linear differential equation:

("d"y)/("d"x) + y/x = sin x

Exercise 10.7 | Q 4 | Page 169

Solve the following Linear differential equation:

(x^2 + 1) ("d"y)/("d"x) + 2xy = sqrt(x^2 + 4)

Exercise 10.7 | Q 5 | Page 169

Solve the following Linear differential equation:

(2x – 10y3)dy + y dx = 0

Exercise 10.7 | Q 6 | Page 169

Solve the following Linear differential equation:

x sin x ("d"y)/("d"x) + (x cos x + sin x)y = sinx

Exercise 10.7 | Q 7 | Page 169

Solve the following Linear differential equation:

(y - "e"^(sin^-1)x) ("d"x)/("d"y) + sqrt(1 - x^2) = 0

Exercise 10.7 | Q 8 | Page 169

Solve the following Linear differential equation:

("d"y)/("d"x) + y/((1 - x)sqrt(x)) = 1 - sqrt(x)

Exercise 10.7 | Q 9 | Page 169

Solve the following Linear differential equation:

(1 + x + xy^2) ("d"y)/("d"x) + (y + y^3) = 0

Exercise 10.7 | Q 10 | Page 169

Solve the following Linear differential equation:

("d"y)/("d"x) + y/(xlogx) = (sin2x)/logx

Exercise 10.7 | Q 11 | Page 169

Solve the following Linear differential equation:

(x + "a") ("d"y)/("d"x) - 2y = (x + "a")^4

Exercise 10.7 | Q 12 | Page 169

Solve the following Linear differential equation:

("d"y)/("d"x) = (sin^2x)/(1 + x^3) - (3x^2)/(1 + x^3) y

Exercise 10.7 | Q 13 | Page 169

Solve the following Linear differential equation:

x ("d"y)/("d"x) + y = x log x

Exercise 10.7 | Q 14 | Page 169

Solve the following Linear differential equation:

x ("d"y)/("d"x) + 2y - x^2 log x = 0

Exercise 10.7 | Q 15 | Page 169

Solve the following Linear differential equation:

("d"y)/("d"x) + (3y)/x = 1/x^2, given that y = 2 when x = 1

Exercise 10.8 [Pages 174 - 175]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide Chapter 10 Ordinary Differential Equations Exercise 10.8 [Pages 174 - 175]

Exercise 10.8 | Q 1 | Page 174

The rate of increase in the number of bacteria in a certain bacteria culture is proportional to the number present. Given that the number triples in 5 hours, find how many bacteria will be present after 10 hours?

Exercise 10.8 | Q 2 | Page 174

Find the population of a city at any time t, given that the rate of increase of population is proportional to the population at that instant and that in a period of 40 years the population increased from 3,00,000 to 4,00,000

Exercise 10.8 | Q 3 | Page 174

The equation of electromotive force for an electric circuit containing resistance and self-inductance is E = "Ri"  + "L" "di"/"dt", where E is the electromotive force is given to the circuit, R the resistance and L, the coefficient of induction. Find the current i at time t when E = 0

Exercise 10.8 | Q 4 | Page 174

The engine of a motor boat moving at 10 m/s is shut off. Given that the retardation at any subsequent time (after shutting off the engine) equal to the velocity at that time. Find the velocity after 2 seconds of switching off the engine

Exercise 10.8 | Q 5 | Page 174

Suppose a person deposits ₹ 10,000 in a bank account at the rate of 5% per annum compounded continuously. How much money will be in his bank account 18 months later?

Exercise 10.8 | Q 6 | Page 174

Assume that the rate at which radioactive nuclei decay is proportional to the number of such nuclei that are present in a given sample. In a certain sample, 10% of the original number of radioactive nuclei have undergone disintegration in a period of 100 years. What percentage of the original radioactive nuclei will remain after 1000 years?

Exercise 10.8 | Q 7. (i) | Page 174

Water at temperature 100°C cools in 10 minutes to 80°C at a room temperature of 25°C. Find the temperature of the water after 20 minutes

Exercise 10.8 | Q 7. (ii) | Page 174

Water at temperature 100°C cools in 10 minutes to 80°C at a room temperature of 25°C. Find the time when the temperature is 40°C [log_"e"  11/15 = - 0.3101; log_"e" 5 = 1.6094]

Exercise 10.8 | Q 8. (i) | Page 174

At 10.00 A.M. a woman took a cup of hot instant coffee from her microwave oven and placed it on a nearby kitchen counter to cool. At this instant, the temperature of the coffee was 180°F and 10 minutes later it was 160°F. Assume that the constant temperature of the kitchen was 70°F. What was the temperature of the coffee at 10.15 AM? |log  9/100 = - 0.6061|

Exercise 10.8 | Q 8. (ii) | Page 174

At 10.00 A.M. a woman took a cup of hot instant coffee from her microwave oven and placed it on a nearby kitchen counter to cool. At this instant, the temperature of the coffee was 180°F and 10 minutes later it was 160°F. Assume that the constant temperature of the kitchen was 70°F. The woman likes to drink coffee when its temperature is between130°F and 140°F. between what times should she have drunk the coffee? |log  6/11 =  - 0.2006|

Exercise 10.8 | Q 9 | Page 174

A pot of boiling water at 100°C is removed from a stove at time t = 0 and left to cool in the kitchen. After 5 minutes, the water temperature has decreased to 80° C and another 5 minutes later it has dropped to 65°C. Determine the temperature of the kitchen

Exercise 10.8 | Q 10 | Page 175

A tank initially contains 50 litres of pure water. Starting at time t = 0 a brine containing 2 grams of dissolved salt per litre flows into the tank at the rate of 3 litres per minute. The mixture is kept uniform by stirring and the well-stirred mixture simultaneously flows out of the tank at the same rate. Find the amount of salt present in the tank at any time t > 0

Exercise 10.9 [Pages 175 - 177]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide Chapter 10 Ordinary Differential Equations Exercise 10.9 [Pages 175 - 177]

#### MCQ

Exercise 10.9 | Q 1 | Page 175

Choose the correct alternative:

The order and degree of the differential equation ("d"^2y)/("d"x^2) + (("d"y)/("d"x))^(1/3) + x^(1/4) = 0 are respectively

• 2, 3

• 3, 3

• 2, 6

• 2, 4

Exercise 10.9 | Q 2 | Page 175

Choose the correct alternative:

The differential equation representing the family of curves y = A cos (x + B), where A and B are parameters, is

• ("d"^2y)/("d"x^2) - y = 0

• ("d"^2y)/("d"x^2) + y = 0

• ("d"^2y)/("d"x^2) = 0

• ("d"^2x)/("d"y^2) = 0

Exercise 10.9 | Q 3 | Page 175

Choose the correct alternative:

The order and degree of the differential equation sqrt(sin  ) ("d"x + "d"y) = sqrt(cos  x)  ("d"x - "d"y) is

• 1, 2

• 2, 2

• 1, 1

• 2, 1

Exercise 10.9 | Q 4 | Page 175

Choose the correct alternative:

The order of the differential equation of all circles with centre at (h, k) and radius 'a' is

• 2

• 3

• 4

• 1

Exercise 10.9 | Q 5 | Page 175

Choose the correct alternative:

The differential equation of the family of curves y = Aex + Be-x, where A and B are arbitrary constants is

• ("d"^2y)/(dx^2) + y = 0

• ("d"^2y)/(dx^2) - y = 0

• ("d"y)/("d"x) + y = 0

• ("d"y)/("d"x) - y = 0

Exercise 10.9 | Q 6 | Page 175

Choose the correct alternative:

The general solution of the differential equation ("d"y)/("d"x) = y/x is

• xy = k

• y = k log x

• y = kx

• log y = kx

Exercise 10.9 | Q 7 | Page 175

Choose the correct alternative:

The solution of the differential equation 2x ("d"y)/("d"x) - y = 3 represents

• straight lines

• circles

• parabola

• ellipse

Exercise 10.9 | Q 8 | Page 175

Choose the correct alternative:

The solution of ("d"y)/("d"x) + "p"(x)y = 0 is

• y = "ce"^(int ""x)

• y = "ce"^(-intpdx)

• x = "ce"^(-intpdy)

• x = "ce"^(intpdy)

Exercise 10.9 | Q 9 | Page 175

Choose the correct alternative:

The integrating factor of the differential equation ("d"y)/("d"x) + y = (1 + y)/lambda is

• x/"e"^lambda

• "e"^lambda/x

• lambda"e"^x

• "e"^x

Exercise 10.9 | Q 10 | Page 176

Choose the correct alternative:

The Integrating factor of the differential equation ("d"y)/("d"x) + "P"(x)y = "Q"(x) is x, then p(x)

• x

• x^2/2

• 1/x

• 1/x^2

Exercise 10.9 | Q 11 | Page 176

Choose the correct alternative:

The degree of the differential equation y(x) = 1 +  ("d"y)/("d"x) + 1/(1.2) (("d"y)/("d"x))^2 + 1/(1*2*3) (("d"y)/("d"x))^3 + .... is

• 2

• 3

• 1

• 4

Exercise 10.9 | Q 12 | Page 176

Choose the correct alternative:

If p and q are the order and degree of the differential equation y("d"y)/("d"x) + x^3 (("d"^2y)/("d"x^2)) + xy = cos x, when

• p < q

• p = q

• p > q

• p exists and q does not exist

Exercise 10.9 | Q 13 | Page 176

Choose the correct alternative:

The solution of the differential equation ("d")/("d"x) + 1/sqrt(1 - x^2) = 0 is

• y + sin-1x = c

• x + sin-1y = 0

• y2 + 2sin-1x = c

• x2 + 2sin-1y = 0

Exercise 10.9 | Q 14 | Page 176

Choose the correct alternative:

The solution of the differential equation ("d"y)/("d"x) = 2xy is

• y = "Ce"^(x^2)

• y = 2x^2 + "C"

• y = 2x2 + C

• y = "Ce"^(-x^2) + "c"

Exercise 10.9 | Q 15 | Page 176

Choose the correct alternative:

The general solution of the differential equation log(("d"y)/("d"x)) = x + y is

• ex + ey = C

• ex + e-y = C

• e-x + ey = C

• e-x + e-y = C

Exercise 10.9 | Q 16 | Page 176

Choose the correct alternative:

The solution of ("d"y)/("d"x) = 2^(y - x) is

• 2x + 2y = C

• 2x – 2y = C

• 1/2^x - 1/2^y = C

• x + y = C

Exercise 10.9 | Q 17 | Page 176

Choose the correct alternative:

The solution of the differential equation ("d"y)/("d"x) = y/x + (∅(y/x))/(∅(y/x)) is

• x∅(y/x) = k

• ∅(y/x) = kx

• y∅(y/x) = k

• ∅(y/x) = ky

Exercise 10.9 | Q 18 | Page 176

Choose the correct alternative:

If sin x is the integrating factor of the linear differential equation ("d"y)/("d"x) + "P"y = "Q", then P is

• log sin x

• cos x

• tan x

• cot x

Exercise 10.9 | Q 19 | Page 176

Choose the correct alternative:

The number of arbitrary constants in the general solutions of order n and n +1are respectively

• n – 1, n

• n, n + 1

• n + 1, n + 2

• n + 1, n

Exercise 10.9 | Q 20 | Page 176

Choose the correct alternative:

The number of arbitrary constants in the particular solution of a differential equation of third order is

• 3

• 2

• 1

• 0

Exercise 10.9 | Q 21 | Page 177

Choose the correct alternative:

Integrating factor of the differential equation ("d"y)/("d"x) = (x + y + 1)/(x + 1) is

• 1/(x + 1)

• x + 1

• 1/sqrt(x + 1)

• sqrt(x + 1)

Exercise 10.9 | Q 22 | Page 177

Choose the correct alternative:

The population P in any year t is such that the rate of increase in the population is proportional to the population. Then

• P = Cekt

• P = Ce-kt

• P = Ckt

• P = Ckt

Exercise 10.9 | Q 23 | Page 177

Choose the correct alternative:

P is the amount of certain substance left in after time t. If the rate of evaporation of the substance is proportional to the amount remaining, then

• P = Cekt

• P = Ce-kt

• P = Ckt

• Pt = C

Exercise 10.9 | Q 24 | Page 177

Choose the correct alternative:

If the solution of the differential equation ("d"y)/("d"x) = ("a"x + 3)/(2y + f) represents a circle, then the value of a is

• 2

• −2

• 1

• −1

Exercise 10.9 | Q 25 | Page 177

Choose the correct alternative:

The slope at any point of a curve y = f(x) is given by ("d"y)/("d"x) - 3x^2 and it passes through (-1, 1). Then the equation of the curve is

• y = x3 + 2

• y = 3x2 + 4

• y = 3x3 + 4

• y = x3 + 5

## Solutions for Chapter 10: Ordinary Differential Equations

Exercise 10.1Exercise 10.2Exercise 10.3Exercise 10.4Exercise 10.5Exercise 10.6Exercise 10.7Exercise 10.8Exercise 10.9 ## Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide chapter 10 - Ordinary Differential Equations

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Concepts covered in Class 12th Mathematics Volume 1 and 2 Answers Guide chapter 10 Ordinary Differential Equations are Introduction to Ordinary Differential Equations, Differential Equation, Order, and Degree, Classification of Differential Equations, Formation of Differential Equations, Solution of Ordinary Differential Equations, Solution of First Order and First Degree Differential Equations, First Order Linear Differential Equations, Applications of First Order Ordinary Differential Equations.

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