The Miscellaneous Exercise of NCERT Solutions for Class 12 Maths Chapter 9- Differential Equations consists of questions that covers all the topic in the chapter. Hence, the exercise is based on the following topics:
- Introduction to Differential Equations
- Basic Concepts of Differential Equation
- General and Particular Solutions of a Differential Equation
- Formation of a Differential Equation whose General Solution is given
- Methods of Solving First Order, First Degree Differential Equations
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Access Answers of Maths 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).
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.
3. Form the differential equation representing the family of curves given by (x – a)2 + 2y2 = a2, where a is an arbitrary constant.
4. Prove that x2 – y2 = c (x2 + y2)2 is the general solution of differential equation (x3–3xy2) dx = (y3–3x2y) dy, where c is a parameter.
5. Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.
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)2 + (y –a)2 = a2 …………1
Now differentiating above equation with respect to x, we get,
2(x-a) + 2(y-a) dy/dx = 0
⇒ (x – a) + (y – a) y’ = 0
On multiplying we get
⇒ x – a +yy’ – ay’ = 0
⇒ x + yy’ –a (1+y’) = 0
Therefore from above equation we have
6. Find the general solution of the differential equation
On integrating, we get,
⇒ sin-1x + sin-1y = C
7. Show that the general solution of the differential equation
is given by (x + y + 1) = A (1 – x – y – 2xy), where A is parameter.
8. Find the equation of the curve passing through the point (0, π/4) whose differential equation is sin x cos y dx + cos x sin y dy = 0.
9. Find the particular solution of the differential equation (1 + e2x) dy + (1 + y2) ex dx = 0, given that y = 1 when x = 0.
10. Solve the differential equation
11. Find a particular solution of the differential equation (x – y) (dx + dy) = dx – dy, given that y = –1, when x = 0. (Hint: put x – y = t)
12. Solve the differential equation
13. Find a particular solution of the differential equation
(x ≠ 0), given that y = 0 when x = π/2
14. Find a particular solution of the differential equation,
given that y = 0 when x = 0.
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?
16. The general solution of the differential equation is
A. xy = C B. x = Cy2 C. y = Cx D. y = Cx2
C. y = Cx
Given question is
17. The general solution of a differential equation of the type is
18. The general solution of the differential equation ex dy + (y ex + 2x) dx = 0 is
A. x ey + x2 = C B. x ey + y2 = C C. y ex + x2 = C D. y ey + x2 = C
C. y ex + x2 = C
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