# Diff. Eq. change of variable

• Dec 2nd 2008, 10:29 AM
diablo2121
Diff. Eq. change of variable
$\displaystyle y ' = x + y$

$\displaystyle u = x + y$

We're supposed to solve the eq. using u, but we have not covered change of variables in class, and I'm having troubles with partial derivatives.

$\displaystyle \frac{du}{dx} = dx + y$

$\displaystyle \frac{du}{dy} = x + dy$

Differentiating in terms of x and y leave those, but I don't know what to do with those. We're trying to find $\displaystyle \frac{dy}{dx}$, but I can't seem to find that in terms of u and x.
• Dec 2nd 2008, 10:41 AM
running-gag
Quote:

Originally Posted by diablo2121
$\displaystyle y ' = x + y$

$\displaystyle u = x + y$

We're supposed to solve the eq. using u, but we have not covered change of variables in class, and I'm having troubles with partial derivatives.

$\displaystyle \frac{du}{dx} = dx + y$

$\displaystyle \frac{du}{dy} = x + dy$

Differentiating in terms of x and y leave those, but I don't know what to do with those. We're trying to find $\displaystyle \frac{dy}{dx}$, but I can't seem to find that in terms of u and x.

Hi

I suppose u and y are functions of x
$\displaystyle \frac{du}{dx} = 1 + \frac{dy}{dx}$ and $\displaystyle \frac{dy}{dx} = x + y$

So $\displaystyle \frac{du}{dx} = 1 + u$
This is a 1st order differential equation