Making a change of variable to transform an equation

Question

1. $\displaystyle m\frac {dv} {dt} = mg - kv^2$
2. $\displaystyle\frac {dV}{dT} = 1 - V^2$

Make a change of variable $v=aV$ and $t=bT$, show that for suitable choices of the parameters $a>0$ and $b>0$ , Equation $1$ maybe be transformed into equation $2$. Both $V$ and $T$ are non-dimensional quantities.