Question

Find the general solution of the given differential equation. dy dx + y = e5x

Answer 1

$\dfrac{\mathrm dy}{\mathrm dx}+y=e^{5x}$
$e^x\dfrac{\mathrm dy}{\mathrm dx}+e^xy=e^{6x}$
$\dfrac{\mathrm d(e^xy)}{\mathrm dx}=e^{6x}$
$e^xy=\displaystyle\int e^{6x}\,\mathrm dx$
$e^xy=\dfrac16e^{6x}+C$
$y=\dfrac16e^{5x}+Ce^{-x}$