# Substituting into a differential equation

• August 30th 2009, 12:10 PM
Paul616
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}
$
• August 30th 2009, 12:13 PM
Matt Westwood
Standard Bernoulii diffeq: set $u - y^{-3}$ and see what happens.