Question

The integrating factor for the differential equation
$\frac{dy}{dx}+xy=\sin \left(x\right)$ is

Answer 1

The given differential equation is an First order linear Differential equation
$\frac{dy}{dx}+Py=Q$
In which P and Q are functions of x with
$I.F.=e^{\int Pdx}$
Therefore for $\frac{dy}{dx}+xy=\sin \left(x\right)$
we get, $P=x$
$\therefore I.F.=e^{\int xdx}$
$\therefore I.F.=e^{\frac{x^2}{2}}$