Question

Find the integrating factor for the differential equation
$\frac{dy}{dx}+\frac{y}{2\sqrt{x}}-\sin x=0$

Answer 1

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

Compare it with standard form
$\frac{dy}{dx}+Py=Q$, where $P$ and $Q$ are functions of $x$, we get
$P=\frac{1}{2\sqrt{x}}$

Integrating factor is given as,
$I.F.=e^{\int Pdx}$
$\therefore I.F.=e^{\int \frac{1}{2\sqrt{x}}dx}$
$\Rightarrow I.F.=e^{\sqrt{x}}$