Question

Find general solution of D.E
$\frac{dy}{dx}=x^{2}y+y$

Answer 1

We have,

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

$\frac{dy}{dx}=(x^2+1)y$

$\frac{dy}{y}=(x^2+1)dx$

On taking integration both sides, we get

$\int \frac{dy}{y}=\int (x^2+1)dx$

$\ln y=\frac{x^3}{3}+x+C$

Hence, this is the answer.