Differential equations special substitutions

**acevipa** · September 2nd 2010, 07:51 PM

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 $\dfrac{dy}{du}$ ?

**TKHunny** · September 2nd 2010, 08:09 PM

Why would you need that? $\dfrac{du}{dx}\;=\;\dfrac{dy}{dx} - 1$ is good enough, isn't it?

**acevipa** · September 2nd 2010, 08:24 PM

So would $\dfrac{du}{dx}=u^2-1$

**Ackbeet** · September 3rd 2010, 02:18 AM

Looks good so far.

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