Question

Find the general solution of the differential equation
$\frac{dy}{dx}-y=sinx$.

Answer 1

Given equation $\frac{dy}{dx}-y=sinx$ represents linear equation

The integration factor is $e^{-x}$

So the solution of differential equation is $y{e}^{-x}=\int e^{-x}sinxdx+c$ , where $c$ is constant

$\Rightarrow y{e}^{-x}=-\frac{e^{-x}}{2}(sinx+cosx)+c$

$\Rightarrow y=-\frac{sinx+cosx}{2}+c{e}^x$