Find the general solution of `(dy)/(dx)+ay=e^(mx)`

Explanation

Given differential equation is `(dy)/(dx)+ay=e^(mx)`
Which is a linear differential equation,
On comparing it with `(dy)/(dx)+Py=Q`, we get
`P=a,Q=e^(mx)`
`IF=e^(intPdx)=e^(intadx)=e^(ax)`
The general solution is `y.e^(ax)=inte^(mx)=e^(ax)=dx+c`
`Rightarrow y.e^(ax)=inte^(m+a)dx+c`
`Rightarrow y.e^(ax)=inte^((m+ax)x)dx+C`
`Rightarrowy.e^(ax)=(e^((m+a)))/((m+a))+C`
`Rightarrow (m+a)y=e^(mx)+Ke^(-ax)`