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CBSE - Class 12 Mathematics Differential Equations Worksheet

The solution of $\frac{dy}{dx} + y = e^{-x}, y (0) = 0$ is :

a. $y = e^{-x} (x – 1)$ b. $y = x e^x$ c. $y = xe^{-x} + 1$ d. $y = xe^{-x}$

Fill in the blanks: The number of arbitrary constants in the general solution of a differential equation of order three is _________.

The general solution of $e^x \cos y dx – e^x \sin y dy = 0$ is :

a. $e^x \cos y = k$ b. $e^x \sin y = k$ c. $e^x = k \cos y$ d. $e^x = k \sin y$

Find the general solution of $\frac{dy}{dx} + ay = e^{mx}$.

Fill in the blanks: The solution of differential equation $\cot y dx = xdy$ is _________.

Solve : $x\frac{dy}{dx} = y (\log y – \log x + 1)$

Fill in the blanks: General solution of $\frac{dy}{dx} + \frac{y}{x} = \sin x$ is _________.

Family $y = Ax + A^3$ of curves will correspond to a differential equation of order

a. 3 b. 2 c. 1 d. not defined

Solution of $\frac{dy}{dx} - y = 1$, $y (0) = 1$ is given by

a. $xy = – e^x$ b. $xy = – e^{-x}$ c. $xy = – 1$ d. $y = 2 e^x – 1$

10.

Solve : $x^2\frac{dy}{dx} = x^2 + xy + y^2$.

11.

Find the general solution of the differential equation $(1 + y^2) + (x – e^{\tan^{-1}y})\frac{dy}{dx} = 0$.

12.

Solve the differential equation $\frac{dy}{dx} + 2xy = y^2$.

13.

The order and degree of the differential equation $(\frac{d^3y}{dx^3})^2 - 3(\frac{d^2y}{dx^2}) + 2(\frac{dy}{dx})^4 = y$ are :

a. 1, 4 b. 3, 4 c. 2, 4 d. 3, 2

14.

Fill in the blanks: $\frac{dy}{dx} + \frac{y}{x\log x} = \frac{1}{x}$ is an equation of the type _________.

15.

Solution of differential equation $xdy – ydx = 0$ represents :

a. a rectangular hyperbola b. parabola whose vertex is at origin c. straight line passing through origin d. a circle whose centre is at origin

16.

State True or False: Number of arbitrary constants in the particular solution of a differential equation of order two is two.

17.

The degree of the differential equation $(\frac{d^2y}{dx^2})^2 + (\frac{dy}{dx})^3 + y^5 + 6 = 0$ is :

a. 1 b. 2 c. 3 d. 5

18.

Fill in the blanks: The solution of the differential equation $x\frac{dy}{dx} + 2y = x^2$ is _________.

19.

Solve the differential equation $(x^2 – 1) \frac{dy}{dx} + 2xy = \frac{1}{x^2 - 1}$.

20.

Which of the following is a second order differential equation?

a. $(y?)^2 + x = y^2$ b. $y?y? + y = \sin x$ c. $y?? + (y?)^2 + y = 0$ d. $y? = y^2$

Worksheet Answers

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