List of top Mathematics Questions on Differential Equations asked in Bihar Board XII

Solve: \[ (1+x^2) \frac{dy}{dx} + y = \tan^{-1} x. \]
Solve the differential equation \[ \frac{dy}{dx} = e^{x + y}. \]
Solve the differential equation: \[ x^2 \frac{dy}{dx} = 2xy. \]
Solve the differential equation: \[ \frac{dx}{dy} = \frac{x}{y} \]
Solve the differential equation: \[ \frac{dx}{dy} + 2y = e^{3x} \]
Solve the differential equation: \[ \frac{dx}{dy} = e^{x + y} \]
Solve the equation: \[ \frac{dx}{dy} + 2y = \sin x \]
Find the order and degree of the differential equation: \[ xy \left( \frac{d^2y}{dx^2} \right) + x \left( \frac{dy}{dx} \right)^2 - y \frac{dy}{dx} = 0 \]
The solution of the differential equation \(x^2\,dx+y^2\,dy=0\) is
Solve \(e^{3x}\,dx+e^{4y}\,dy=0\).
The solution of \(\dfrac{dx}{x}+\dfrac{dy}{y}=0\) is
The integrating factor of the linear DE \(\dfrac{dy}{dx}-y\sin x=\cot x\) is
The integrating factor of the linear DE \(\dfrac{dy}{dx}+\dfrac{2}{x}y=5x^{2}\) is
The solution of the differential equation \(dx+dy=0\) is