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Chapters
1.2: Matrics
1.3: Trigonometric Functions
1.4: Pair of Lines
1.5: Vectors and Three Dimensional Geometry
1.6: Line and Plane
1.7: Linear Programming Problems
2.1: Differentiation
2.2: Applications of Derivatives
2.3: Indefinite Integration
2.4: Definite Integration
2.5: Application of Definite Integration
▶ 2.6: Differential Equations
2.7: Probability Distributions
2.8: Binomial Distribution
![SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC chapter 2.6 - Differential Equations - Shaalaa.com](/images/mathematics-and-statistics-arts-and-science-english-12-standard-hsc_6:5f2b1b2038084cf381bfa42c826a928c.jpg "SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC chapter 2.6 - Differential Equations")
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Solutions for Chapter 2.6: Differential Equations
Below listed, you can find solutions for Chapter 2.6 of Maharashtra State Board SCERT Maharashtra for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC.
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 2.6 Differential Equations MCQ
2 Marks
Select and write the correct alternative from the given option for the question
Solution of the equation `x ("d"y)/("d"x)` = y log y is
y = aex
y = be2x
y = be−2x
y = eax
Select and write the correct alternative from the given option for the question
Bacterial increases at the rate proportional to the number present. If original number M doubles in 3 hours, then number of bacteria will be 4M in
4 hours
6 hours
8 hours
10 hours
The general solution of `(dy)/(dx)` = e−x is ______.
y = ex + c
y = e–x + c
y = – e–x + c
y = e2x + c
Select and write the correct alternative from the given option for the question
The differential equation of y = Ae5x + Be–5x is
`("d"^2y)/("d"x^2)` = 25y
`("d"^2y)/("d"x^2)` = – 25y
`("d"^2y)/("d"x^2)` = 5y
`y ("d"^2y)/("d"x^2)` = – 5y
Select and write the correct alternative from the given option for the question
Differential equation of the function c + 4yx = 0 is
`xy + ("d"y)/("d"x)` = 0
`x ("d"y)/("d"x) + y` = 0
`("d"y)/("d"x) - 4xy` = 0
`x ("d"y)/("d"x) + 1` = 0
Select and write the correct alternative from the given option for the question
General solution of `y - x ("d"y)/("d"x)` = 0 is
`3log x + 7/y` = c
`2logx + 3/y` = c
log x – log y = log c
`3log y + 2/x` = c
Select and write the correct alternative from the given option for the question
The order and degree of `(("d"y)/("d"x))^3 - ("d"^3y)/("d"x^3) + y"e"^x` = 0 are respectively
3, 1
1, 3
3, 3
1, 1
Select and write the correct alternative from the given option for the question
The order and degree of `(1 + (("d"y)/("d"x))^3)^(2/3) = 8 ("d"^3y)/("d"x^3)` are respectively
3, 1
1, 3
3, 3
1, 1
Select and write the correct alternative from the given option for the question
The solution of `("d"y)/("d"x)` = 1 is
x + y = c
xy = c
x2 + y2 = c
y – x = c
Select and write the correct alternative from the given option for the question
The solutiion of `("d"y)/("d"x) + x^2/y^2` = 0 is
x3 + y3 = 7
x2 + y2 = c
x3 + y3 = c
x + y = c
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 2.6 Differential Equations Answer the following
1 Mark
Find the differential equation of family of lines making equal intercepts on coordinate axes
Find the general solution of `("d"y)/("d"x) = (1 + y^2)/(1 + x^2)`
Form the differential equation of family of standard circle
State the degree of differential equation `e^((dy)/(dx)) + (dy)/(dx)` = x
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 2.6 Differential Equations Attempt the following questions I
2 Marks
Form the differential equation of y = (c1 + c2)ex
Solve the differential equation sec2y tan x dy + sec2x tan y dx = 0
Find the differential equation of family of all ellipse whose major axis is twice the minor axis
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 2.6 Differential Equations Attempt the following questions II
3 Marks
Solve the differential equation `("d"y)/("d"x) + y` = e−x
Solve the following differential equation:
`"x" "dy"/"dx" + "2y" = "x"^2 * log "x"`
Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`
Solve the differential equation xdx + 2ydy = 0
Solve the differential equation (x2 – yx2)dy + (y2 + xy2)dx = 0
Solve the following differential equation `("d"y)/("d"x)` = x2y + y
Find the differential equation by eliminating arbitrary constants from the relation x2 + y2 = 2ax
Find the differential equation by eliminating arbitrary constants from the relation y = (c1 + c2x)ex
Verify y = log x + c is the solution of differential equation `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0
Solve: `("d"y)/("d"x) + 2/xy` = x2
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 2.6 Differential Equations Attempt the following questions III
4 Marks
For the differential equation, find the particular solution (x – y2x) dx – (y + x2y) dy = 0 when x = 2, y = 0
Solve the following differential equation:
`"dy"/"dx" + ("x" - "2y")/("2x" - "y") = 0`
Find the differential equation from the relation x2 + 4y2 = 4b2
If the population of a town increases at a rate proportional to the population at that time. If the population increases from 40 thousand to 60 thousand in 40 years, what will be the population in another 20 years? `("Given" sqrt(3/2) = 1.2247)`
The rate of growth of bacteria is proportional to the number present. If initially, there were 1000 bacteria and the number doubles in 1 hour, find the number of bacteria after `5/2` hours `("Given" sqrt(2) = 1.414)`
Solve the following differential equation
`yx ("d"y)/("d"x)` = x2 + 2y2
Solve the following differential equation y log y = `(log y - x) ("d"y)/("d"x)`
For the differential equation, find the particular solution
`("d"y)/("d"x)` = (4x +y + 1), when y = 1, x = 0
Solve the following differential equation y2dx + (xy + x2) dy = 0
Solve the following differential equation
`x^2 ("d"y)/("d"x)` = x2 + xy − y2
Solutions for 2.6: Differential Equations
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC chapter 2.6 - Differential Equations
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Concepts covered in Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC chapter 2.6 Differential Equations are Basic Concepts of Differential Equations, Order and Degree of a Differential Equation, Formation of Differential Equations, Solution of a Differential Equation, Methods of Solving Differential Equations> Homogeneous Differential Equations, Methods of Solving Differential Equations>Linear Differential Equations, Applications of Differential Equation, Overview of Differential Equations.
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