# Thread: Substituting into a differential equation

1. ## Substituting into a differential equation

Use $y = u^k$ to prove

$\frac{dy}{dx}= y - (y^4)x$

can be rewritten as

$
\frac{d}{dx} (e^{3x}u) = 3xe^{3x}
$

2. Standard Bernoulii diffeq: set $u - y^{-3}$ and see what happens.