# NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Miscellaneous Exercise

## NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Miscellaneous Exercise â€“ CBSE Term II Free PDF Download

The Miscellaneous Exercise of NCERT Solutions for Class 12 Maths Chapter 9- Differential Equations consists of questions that cover all the topics in the chapter. Hence, the exercise is based on the following topics:

1. Introduction to Differential Equations
2. Basic Concepts of Differential Equation
3. General and Particular Solutions of a Differential Equation
4. Formation of a Differential Equation whose General Solution is given
5. Methods of Solving First Order, First Degree Differential Equations

## Download PDF of NCERT Solutions for Class 12 Maths Chapter 9- Differential Equations Miscellaneous Exercise

### Access Answers to NCERT Class 12 Maths Chapter 9- Differential Equations Miscellaneous Exercise Page Number 419

1. For each of the differential equations given below, indicate its order and degree (if defined).

Solution:

Therefore, its degree is three.

2. For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.

Solution:

3. Form the differential equation representing the family of curves given by (x â€“ a)2Â + 2y2Â = a2, where a is an arbitrary constant.

Solution:

4. Prove that x2Â â€“ y2Â = c (x2Â + y2)2Â is the general solution of differential equation (x3â€“3xy2) dx = (y3â€“3x2y) dy, where c is a parameter.

Solution:

5. Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.

Solution:

We know that the equation of a circle in the first quadrant with centre (a, a) and radius a which touches the coordinate axes is (x -a)2Â + (y â€“a)2Â = a2Â â€¦â€¦â€¦â€¦1

Now differentiating above equation with respect to x, we get,

2(x-a) + 2(y-a) dy/dxÂ = 0

â‡’Â (x â€“ a) + (y â€“ a) yâ€™ = 0

On multiplying we get

â‡’Â x â€“ a +yyâ€™ â€“ ayâ€™ = 0

â‡’Â x + yyâ€™ â€“a (1+yâ€™) = 0

Therefore from above equation we have

6. Find the general solution of the differential equation

Solution:

On integrating, we get,

â‡’Â sin-1x + sin-1y = C

7. Show that the general solution of the differential equation

is given by (x + y + 1) = A (1 â€“ x â€“ y â€“ 2xy), where A is parameter.

Solution:

8. Find the equation of the curve passing through the pointÂ (0, Ï€/4)Â whose differential equation is sin x cos y dx + cos x sin y dy = 0.

Solution:

9. Find the particular solution of the differential equation (1 + e2x) dy + (1 + y2) exÂ dx = 0, given that y = 1 when x = 0.

Solution:

10. Solve the differential equation

Solution:

11. Find a particular solution of the differential equation (x â€“ y) (dx + dy) = dx â€“ dy, given that y = â€“1, when x = 0. (Hint: put x â€“ y = t)

Solution:

12. Solve the differential equation

Solution:

13. Find a particular solution of the differential equationÂ

(x â‰  0), given that y = 0 whenÂ x = Ï€/2

Solution:

14. Find a particular solution of the differential equation,

given that y = 0 when x = 0.

Solution:

15. The population of a village increases continuously at the rate proportional to the number of its inhabitants present at any time. If the population of the village was 20, 000 in 1999 and 25000 in the year 2004, what will be the population of the village in 2009?

Solution:

16. The general solution of the differential equationÂ Â  is
A. xy = C B. x = Cy2 C. y = Cx D. y = Cx2

Solution:

C. y = Cx

Explanation:

Given question is

17. The general solution of a differential equation of the type is

Solution:

Explanation:

18. The general solution of the differential equation exÂ dy + (y exÂ + 2x) dx = 0 is
A. x ey + x2Â = C B. x ey + y2Â = C C. y ex + x2Â = C D. y ey + x2Â = C

Solution:

C. y ex + x2Â = C

Explanation:

#### Access Other Exercise Solutions of Class 12 Maths Chapter 9- Differential Equations Miscellaneous Exercise

Exercise 9.1 Solutions 12 Questions

Exercise 9.2 Solutions 12 Questions

Exercise 9.3 Solutions 12 Questions

Exercise 9.4 Solutions 23 Questions

Exercise 9.5 Solutions 17 Questions

Exercise 9.6 Solutions 19 Questions