Solution of the differential equation $\frac{dy}{dx}+ay=e^{mx}$ is :
Answer & explanation
Correct answer: option 1
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)
$∫e^{ax}\frac{dy}{dx}+ae^{ax}ydx=∫e^{(a+m)x}dx$
$⇒ye^{ax}=\frac{e^{(a+m)x}}{(a+m)}+C$
$⇒y(a+m)=e^{mx}+c'e^{-ax}$