Solution of the differential equation $\frac{dy}{dx}+ay=e^{mx}$ is :

$(a+m)y=e^{mx}+Ce^{-ax}$

The correct answer is option (1) → $(a+m)y=e^{mx}+Ce^{-ax}$

$I.F.=e^{∫adx}=e^{ax}$

multiplying eq. with I.F. and differentiating wrt (x)

$∫e^{ax}\frac{dy}{dx}+ae^{ax}ydx=∫e^{(a+m)x}dx$

$⇒ye^{ax}=\frac{e^{(a+m)x}}{(a+m)}+C$

$⇒y(a+m)=e^{mx}+c'e^{-ax}$