Solution of differential equation $\frac{d y}{d x}+a y=e^{m x}$ is :

$(a+m) y=e^{m x}+c e^{-a x}$

I. F. = $e^{\int a d x}=e^{a x}$

∴ Solution is $y . e^{a x}=\int e^{a x} . e^{m x} d x+c_1$

$\Rightarrow y . e^{a x}=\frac{e^{(a+m) x}}{a+m}+c_1$

$\Rightarrow(a+m) y=e^{m x}+c_1(a+m) e^{-a x}$

$\Rightarrow (a+m) y=e^{m x}+c e^{-a x}$

where $c=c_1(a+m)$

Hence (4) is the correct answer.