Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Differential Equations

Long Answer Type

331.

Solve the following differential equation:

$\cos^{2} x \frac{dy}{dx} + y = tanx$

332.

Solve the following differential equation:

$(1 + x^{2}) \frac{dy}{dx} + y = \tan^{- 1} x$

333.

Find the particular solution, satisfying the given condition, for the following differential equation:

$\frac{dy}{dx} - \frac{y}{x} + cosec (\frac{y}{x}) = 0; y = 0 when x = 1$

Short Answer Type

334.

What is the degree of the following differential equation?

5x $5 x {(\frac{dy}{dx})}^{2} - \frac{d^{2} y}{{dx}^{2}} - 6 y = \log x$

Long Answer Type

335.

Find the particular solution of the differential equation satisfying the given conditions: x² dy + (xy + y² )dx = 0; y = 1 when x = 1.

336.

Find the general solution of the differential equation,

$x \log x \frac{dy}{dx} + y = \frac{2}{x} \log x$

337.

Find the particular solution of the differential equation satisfying the given conditions:

$\frac{dy}{dx} = y \tan x$ , given that y = 1 when x= 0.

338.
Solve the following differential equation:
e^x tan y dx + ( 1 - e^x) sec² y dy = 0

The given differential equation is:

e^x tan y dx + ( 1 - e^x) sec² y dy = 0

$\Rightarrow$ e^x tan y dx = - ( 1 - e^x) sec² y dy

$\Rightarrow$ e^x tan y dx = ( e^x - 1 ) sec² y dy

$\Rightarrow \frac{e^{x}}{e^{x} - 1} dx = \frac{\sec^{2} y}{\tan y} dy$

On integrating on both sides, we get

$\int \frac{e^{x}}{e^{x} - 1} dx = \int \frac{\sec^{2} y}{\tan y} dy . . . . . . . . . . (i) Let I_{1} = \int \frac{\sec^{2} y}{\tan y} dy Put \tan y = t \Rightarrow \sec^{2} y dy = dt ∴ \int \frac{\sec^{2} y}{\tan y} dy = \int \frac{dt}{t} = \log |t| = \log \tan y . . . . . . . . . (ii) Let I_{2 =} \int \frac{e^{x}}{e^{x} - 1} dx$