Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions

For the following differential equation, find a particular solution satisfying the given condition:- \[\frac{dy}{dx} = y \tan x, y = 1\text{ when }x = 0\]

Solve the following differential equation:- \[\left( x - y \right)\frac{dy}{dx} = x + 2y\]

Solve the following differential equation:- \[x \cos\left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x\]

Solve the following differential equation:- `y dx + x log  (y)/(x)dy-2x dy=0`

Solve the following differential equation:-

\[\frac{dy}{dx} - y = \cos x\]

Solve the following differential equation:-

\[x\frac{dy}{dx} + 2y = x^2 , x \neq 0\]

Solve the following differential equation:-

\[\frac{dy}{dx} + 2y = \sin x\]

Solve the following differential equation:-

\[\frac{dy}{dx} + 3y = e^{- 2x}\]

Solve the following differential equation:-

\[\frac{dy}{dx} + \frac{y}{x} = x^2\]

Solve the following differential equation:-

\[\frac{dy}{dx} + \left( \sec x \right) y = \tan x\]

Solve the following differential equation:-

\[x\frac{dy}{dx} + 2y = x^2 \log x\]

Solve the following differential equation:-

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

Solve the following differential equation:-

(1 + x²) dy + 2xy dx = cot x dx

Solve the following differential equation:-

\[\left( x + y \right)\frac{dy}{dx} = 1\]

Solve the following differential equation:-

y dx + (x − y²) dy = 0

Solve the following differential equation:-

\[\left( x + 3 y^2 \right)\frac{dy}{dx} = y\]

Find a particular solution of the following differential equation:- \[\left( 1 + x^2 \right)\frac{dy}{dx} + 2xy = \frac{1}{1 + x^2}; y = 0,\text{ when }x = 1\]

Find a particular solution of the following differential equation:- (x + y) dy + (x − y) dx = 0; y = 1 when x = 1

Find a particular solution of the following differential equation:- x² dy + (xy + y²) dx = 0; y = 1 when x = 1

Find the equation of the curve passing through the point (1, 1) whose differential equation is x dy = (2x² + 1) dx, x ≠ 0.