# Differential equations special substitutions

• September 2nd 2010, 07:51 PM
acevipa
Differential equations special substitutions
I'm having some trouble solving this differential equation

Solve $\dfrac{dy}{dx}=(y-x)^2$ using the substitution $u=y-x$

Do I have to find $\dfrac{dy}{du}$?
• September 2nd 2010, 08:09 PM
TKHunny
Why would you need that? $\dfrac{du}{dx}\;=\;\dfrac{dy}{dx} - 1$ is good enough, isn't it?
• September 2nd 2010, 08:24 PM
acevipa
So would $\dfrac{du}{dx}=u^2-1$
• September 3rd 2010, 02:18 AM
Ackbeet
Looks good so far.