# Thread: differential equation help

1. ## differential equation help

du/dt = -u^2(t^3-t)

Find the general solution to the above differential equation. Write the answer in a form such that its numerator is 1 and its integration constant is C

Find the particular solution of the above differential equation that satisfies the condition u=4 at t=0.

2. Originally Posted by derekjonathon
du/dt = -u^2(t^3-t)

Find the general solution to the above differential equation. Write the answer in a form such that its numerator is 1 and its integration constant is C

Find the particular solution of the above differential equation that satisfies the condition u=4 at t=0.
$\int-u^{-2}\,du=\int t^3-t\,dt\implies \frac{1}{u}=\frac{t^4}{4}-\frac{t^2}{2}+C$

The rest is just algebra.