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

For each of the exercises given below, verify that the given function (implicit or explicit)
is a solution of the corresponding differential equation.

i) \(y=ae^x+be^{-x}+x^2: x\frac{d^2y}{dx^2}+2\frac{dy}{dx}-xy+x^2-2=0\)

ii) \(y=e^x(a \cos x+ b \sin x):\frac{d^2y}{dx^2}-2\frac{dy}{dx}+2y=0\)

iii) \(y= x \sin 3x:\frac{d^2y}{dx^2}+9y-6\cos3x=0\)

iv) \(x^2=2y^2\log y:(x^2+y^2)\frac{dy}{dx}-xy=0\)

Find the particular solution of the differential equation \((1+e^{2x})dy+(1+y^2)e^xdx=0\), given that \(y=1 \) when \(x=0\)

Find the general solution of the differential equation:
\(\frac {dy}{dx}+\sqrt {\frac {1-y^2}{1-x^2}}=0\)

Form the differential equation representing the family of curves given by:
\((x-α)^2+2y^2=α^2\) where a is an arbitrary constant.

\(\int_0^\frac \pi2\)\(\frac {\pi}{20} cos\ 2x\ dx\)

Find the general solution: \(\frac {dy}{dx}+2y=sin\ x\)