Arts (English Medium) इयत्ता १२ - CBSE Important Questions

Find the particular solution of the differential equation

`tan x * (dy)/(dx) = 2x tan x + x^2 - y`; `(tan x != 0)` given that y = 0 when `x = pi/2`

Solve the following differential equation:
\[\text{ cosec }x \log y \frac{dy}{dx} + x^2 y^2 = 0\]

Find the general solution of the differential equation \[x \cos \left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x .\]

Find the particular solution of the differential equation `(1+y^2)+(x-e^(tan-1 )y)dy/dx=` given that y = 0 when x = 1.

Solve the following differential equation : \[y^2 dx + \left( x^2 - xy + y^2 \right)dy = 0\] .

Solve the following differential equation: \[\left( \cot^{- 1} y + x \right) dy = \left( 1 + y^2 \right) dx\] .

Write the sum of the order and degree of the differential equation

\[\left( \frac{d^2 y}{{dx}^2} \right)^2 + \left( \frac{dy}{dx} \right)^3 + x^4 = 0 .\]

Write the solution of the differential equation \[\frac{dy}{dx} = 2^{- y}\] .

Solve the following differential equation : \[\left[ y - x  \cos\left( \frac{y}{x} \right) \right]dy + \left[ y  \cos\left( \frac{y}{x} \right) - 2x  \sin\left( \frac{y}{x} \right) \right]dx = 0\] .

Solve the following differential equation : \[\left( \sqrt{1 + x^2 + y^2 + x^2 y^2} \right) dx + xy \ dy = 0\].

Find the particular solution of the differential equation \[\frac{dy}{dx} = \frac{x\left( 2 \log x + 1 \right)}{\sin y + y \cos y}\] given that

If x^myⁿ = (x + y)^m+n, prove that \[\frac{dy}{dx} = \frac{y}{x} .\]

Solve the differential equation (x² − yx²) dy + (y² + x²y²) dx = 0, given that y = 1, when x = 1.

Solve the differential equation \[\frac{dy}{dx}\] + y cot x = 2 cos x, given that y = 0 when x = \[\frac{\pi}{2}\] .

For the following differential equation, find a particular solution satisfying the given condition:

\[x\left( x^2 - 1 \right)\frac{dy}{dx} = 1, y = 0\text{ when }x = 2\]

Find the integerating factor of the differential equation `xdy/dx - 2y = 2x^2` . 

Solve the differential equation: (1 +x² ) dy + 2xy dx = cot x dx 

Write the order and degree of the differential equation `((d^4"y")/(d"x"^4))^2 =  [ "x" + ((d"y")/(d"x"))^2]^3`.

Solve the differential equation: (1 + x²) dy + 2xy dx = cot x dx

Find the area of the region bounded by the curves (x -1)² + y² = 1 and x² + y² = 1, using integration.