The equation of motion of a train is given by $m\frac{\mathrm{dv} }{\mathrm{d} t} = mk(1-e^{-t})-mcv$ where $v$ is the speed,$t$ is the time and $m,k,c$ are constants.How to find $v$ when $v=0$ and $t=0$. This is what i've tried so far $\frac{\mathrm{dv} }{\mathrm{d} t}=k(1-e^{-t}-cv)$ after seperating and factoring $m$.Now I Don't know how to put this in $\frac{\mathrm{dy} }{\mathrm{d} x}+Py = Q$ form and figure out the integrating factor.Please Help.
Thank You.