# Math Help - Seperation of variables

1. ## Seperation of variables

Hi,

I need help integrating this equation;

dv/dt=(-g/b^2)(v^2+b^2)

This is causing me problems. I'd really appreciate a solution/pointer

Thanks

Jem

2. Originally Posted by jemmy
Hi,

I need help integrating this equation;

dv/dt=(-g/b^2)(v^2+b^2)
$v' = (-g/b^2)(v^2+b^2)\implies \frac{v'}{v^2+b^2} = - gb^2$.

Thus, $\int \frac{v'dt}{v^2+b^2} = -\int -gb^2 dt \implies \frac 1b\tan^{-1} \frac{v}{b} + C = -gb^2t$ (assuming b>0).