List of top Mathematics Questions on Differential equations asked in CBSE CLASS XII

The sum of the order and degree of the differential equation \[ \left( 1 + \left( \frac{dy}{dx} \right)^2 \right) \frac{d^2y}{dx^2} = \left( \frac{dy}{dx} \right)^3 \] is:
The sum of the order and degree of the differential equation \[ \left( 1 + \left( \frac{dy}{dx} \right)^2 \right) \frac{d^2y}{dx^2} = \left( \frac{dy}{dx} \right)^3 \] is:
The integrating factor of the differential equation \( \frac{dx}{dy} = \frac{x \log x}{2 \log x - y} \) is:
Solve 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 \( \frac{dy}{dx} - \frac{y}{x} + \csc\left(\frac{y}{x}\right) = 0 \); given that \( y = 0 \), when \( x = 1 \).
The integrating factor of the differential equation \( (x + 2y^2) \frac{dy}{dx} = y \, (y>0) \) is:} 
 
The number of arbitrary constants in the particular solution of the differential equation \[ \log \left( \frac{dy}{dx} \right) = 3x + 4y; \quad y(0) = 0 \] is/are:
The general solution of the differential equation \( x \, dy + y \, dx = 0 \) is:
The integrating factor of the differential equation \[ (x + 2y^2) \frac{dy}{dx} = y, \quad (y > 0) \] is:
Find the particular solution of the differential equation \( \left( x (e)^y/^x + y \right) dx = x \, dy \), given that \( y = 1 \) when \( x = 1 \).
Find the particular solution of the differential equation: \[ \frac{dy}{dx} = y \cot 2x, \] given that \( y\left(\frac{\pi}{4}\right) = 2 \).
Find the particular solution of the differential equation \( \left( x (e)^y/^x + y \right) dx = x \, dy \), given that \( y = 1 \) when \( x = 1 \).
Find the particular solution of the differential equation \( \frac{dy}{dx} = y \cot 2x \), given that \( y\left(\frac{\pi}{4}\right) = 2 \).

The general solution of the differential equation \(e^{x}dy+(ye^{x}+2x)dx=0\) is

The general solution of the differential equation \(\frac{ydx-xdy}{y}=0 \) is

The general solution of a differential equation of the type \(\frac{dx}{dy}+p_{1}x=Q1\) is

Which of the following is a homogenous differential equation?

The integrating factor of the differential equation \(x\frac{dy}{dx}-y=2x^{2}\) is

The integrating factor of the differential equation.
\((1-y^{2})\frac{dx}{dy}+yx=ay\)\((-1<y<1)\)\(is\)
For the differential equations, find the general solution:\(\frac {dy}{dx} =(1+x^2)(1+y^2)\)
For the differential equations , find a particular solution satisfying the given condition:\((x^3+x^2+x+1)\frac{dy}{dx}=2x^2+x;y=1\) when \(x=0\)
Show that the given differential equation is homogeneous and solve:\((x^2+xy)dy=(x^2+y^2)dx\)

Find a particular solution satisfying the given condition:\((1+x^2)\frac {dy}{dx}+2xy=\frac {1}{1+x^2}; \ y=0 \ when \ x=1\) 

The numbers of arbitrary constants in the particular solution of a differential equation of third order are:

Find a particular solution satisfying the given condition: \(\frac {dy}{dx}+2y\ tan\ x=sin\ x;\ y=0\  when \ x=\frac \pi3\)