Samacheer Kalvi solutions for Business Mathematics and Statistics [English] Class 12 TN Board chapter 4 - Differential Equations [Latest edition]

Find the order and degree of the following differential equation:

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

Find the order and degree of the following differential equation:

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

Find the order and degree of the following differential equation:

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

Find the order and degree of the following differential equation:

`("d"^3y)/("d"x^3) = 0`

Find the order and degree of the following differential equation:

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

Find the order and degree of the following differential equation:

(2 – y”)² = y”² + 2y’

Find the order and degree of the following differential equation:

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

Find the differential equation of the following:

y = cx + c – c³

Find the differential equation of the following:

y = c(x – c)²

Find the differential equation of the following:

xy = c² 

Find the differential equation of the following:

x² + y² = a² 

Form the differential equation by eliminating α and β from (x – α)² + (y – β)² = r²

Find the differential equation of the family of all straight lines passing through the origin

Form the differential equation that represents all parabolas each of which has a latus rectum 4a and whose axes are parallel to the x-axis

Find the differential equation of all circles passing through the origin and having their centers on the y axis

Find the differential equation of the family of a parabola with foci at the origin and axis along the x-axis

Solve: `("d"y)/("d"x) = "ae"^y`

Solve: `(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`

Solve: `y(1 - x) - x ("d"y)/("d"x)` = 0

Solve: ydx – xdy = 0 dy

Solve: `("d"y)/("d"x) + "e"^x + y"e"^x = 0`

Solve : cos x(1 + cosy) dx – sin y(1 + sinx) dy = 0

Solve: (1 – x) dy – (1 + y) dx = 0

Solve: `("d"y)/("d"x) = y sin 2x`

Solve: `log(("d"y)/("d"x))` = ax + by

Find the curve whose gradient at any point P(x, y) on it is `(x - "a")/(y - "b")` and which passes through the origin

Solve the following homogeneous differential equation:

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

Solve the following homogeneous differential equation:

`(x - y) ("d"y)/("d"x) = x + 3y`

Solve the following homogeneous differential equation:

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

Solve the following homogeneous differential equation:

`("d"y)/("d"x) = (3x - 2y)/(2x - 3y)`

Solve the following homogeneous differential equation:

(y² – 2xy) dx = (x² – 2xy) dy

Solve the following homogeneous differential equation:

The slope of the tangent to a curve at any point (x, y) on it is given by (y³ – 2yx²) dx + (2xy² – x³) dy = 0 and the curve passes through (1, 2). Find the equation of the curve

Solve the following homogeneous differential equation:

An electric manufacturing company makes small household switches. The company estimates the marginal revenue function for these switches to be (x² + y²) dy = xy dx where x represents the number of units (in thousands). What is the total revenue function?

Solve the following:

`("d"y)/("d"x) - y/x = x`

Solve the following:

`("d"y)/(""dx) + y cos x = sin x cos x`

Solve the following:

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

Solve the following:

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

Solve the following:

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

Solve the following:

`("d"y)/("d"x) + y tan x = cos^3x`

Solve the following:

If `("d"y)/("d"x) + 2 y tan x = sin x` and if y = 0 when x = `pi/3` express y in term of x.

Solve the following:

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

Solve the following:

A bank pays interest by continuous compounding, that is by treating the interest rate as the instantaneous rate of change of principal. A man invests ₹ 1,00,000 in the bank deposit which accrues interest, 8% per year compounded continuously. How much will he get after 10 years? (e^0.8 = 2.2255)

Solve the following differential equation:

`("d"^2y)/("d"x^2) - 6 ("d"y)/("d"x) + 8y = 0`

Solve the following differential equation:

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

Solve the following differential equation:

(D² + 2D + 3)y = 0

Solve the following differential equation:

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

Solve the following differential equation:

(D² – 2D – 15)y = 0 given that `("d"y)/("d"x)` = 0 and `("d"^2y)/("d"x^2)` = 2 when x = 0

Solve the following differential equation:

(4D² + 4D – 3)y = e^2x

Solve the following differential equation:

`("d"^2y)/("d"x^2) + 16y = 0`

Solve the following differential equation:

(D² – 3D + 2)y = e^3x which shall vanish for x = 0 and for x = log 2

Solve the following differential equation:

(D² + D – 2)y = e^3x + e^–3x 

Solve the following differential equation:

(D² – 10D + 25) y = 4e^5x + 5

Solve the following differential equation:

`(4"D"^2 + 16"D" + 15)y = 4"e"^((-3)/2x)`

Solve the following differential equation:

(3D² + D – 14)y – 13e^2x

Solve the following differential equation:

Suppose that the quantity demanded Q_d = `13 - 6"p" + 2 "dp"/"dt" + ("d"^2"p")/("dt"^2)` and quantity supplied Q_s = `- 3 + 2"p"` where p is the price. Find the equilibrium price for market clearance

Choose the correct alternative:

The degree of the differential equation `("d"^4y)/("d"x^4) - (("d"^2y)/("d"x^2))^4 + ("d"y)/("d"x) = 3`

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The order and degree of the differential equation `sqrt(("d"^2y)/("d"x^2)) = sqrt(("d"y)/("d"x) + 5)` are respectively

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

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Th e differential equation `(("d"x)/("d"y))^3 + 2y^(1/2) = x` is

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The differential equation formed by eliminating a and b from y = ae^x + be^-x is

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If y = ex + c – c³ then its differential equation is

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The integrating factor of the differential equation `("d"y)/("d"x) + "P"x` = Q is

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The complementary function of (D² + 4) y = e^2x is

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The differential equation of y = mx + c is (m and c are arbitrary constants)

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The particular intergral of the differential equation `("d"^2y)/("d"x^2) - 8 ("d"y)/("d"x) + 16y = 2"e"^(4x)`

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Solution of `("d"x)/("d"y) + "P"x = 0`

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If sec² x is an integrating factor of the differential equation `("d"y)/("d"x) + "P"y` = Q then P = 

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The integrating factor of `x ("d"y)/("d"x) - y = x^2` is

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The solution of the differential equation `("d"y)/("d"x) + "P"y` = Q where P and Q are the function of x is

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The differential equation formed by eliminating A and B from y = e^-2x (A cos x + B sin x) is

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The particular integral of the differential equation f(D) y = e^ax where f(D) = (D – a)² 

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The differential equation of x² + y² = a²

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The complementary function of `("d"^2y)/("d"x^2) - ("d"y)/("d"x) = 0` is

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The P.I of (3D² + D – 14)y = 13e^2x is

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

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A homogeneous differential equation of the form `("d"y)/("d"x) = f(y/x)` can be solved by making substitution

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A homogeneous differential equation of the form `("d"x)/("d"y) = f(x/y)` can be solved by making substitution

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The variable separable form of `("d"y)/("d"x) = (y(x - y))/(x(x + y))` by taking y = vx and `("d"y)/("d"x) = "v" + x "dv"/("d"x)` is

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Which of the following is the homogeneous differential equation?

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

Suppose that Q_d = `30 - 5"P" + 2 "dP"/"dt" + ("d"^2"P")/("dt"^2)` and Q_s = 6 + 3P. Find the equilibrium price for market clearance

Form the differential equation having for its general solution y = ax² + bx

Solve yx²dx + e^–x dy = 0

Solve (x² + y²) dx + 2xy dy = 0

Solve `x ("d"y)/(d"x) + 2y = x^4`

A manufacturing company has found that the cost C of operating and maintaining the equipment is related to the length ’m’ of intervals between overhauls by the equation `"m"^2 "dC"/"dm" + 2"mC"` = 2 and c = 4 and when  = 2. Find the relationship between C and m

Solve (D² – 3D + 2)y = e^4x given y = 0 when x = 0 and x = 1

Solve `("d"y)/("d"x) + y cos x + x = 2 cos x`

Solve x²ydx – (x³ + y³) dy = 0

Solve `("d"y)/("d"x) = xy + x + y + 1`