Partial differential equation

1. Oct 26, 2005

Beer-monster

Hi does anyone know how to solve this partial differential equation. My brain appears to be burping (and strangely my past notes don't seem to have any similar equation in)
$$\frac{\partial{\psi}}{\partial{x}} = k(x+y)$$
Anyone know any good tutorials or webpages for these sorts of equation? I'm a bit rusty with them

2. Oct 26, 2005

mathmike

3. Oct 26, 2005

HallsofIvy

Staff Emeritus
$$\frac{\partial{\psi}}{\partial{x}} = k(x+y)$$

Since x and y are independent, all you can do is integrate, with respect to x, treating y as a constant:
$$\psi(x,y)= \frac{k}{2}x^2+ yx+ f(y)$$
Since the partial derivative wrt x is taken treating y as a constant, f(y) could be any function of y alone- its derivative will be 0.

4. Oct 26, 2005

Beer-monster

I tried that but didn't get the right answer, I'll give it another shot.

Although isn't the second term kyx as it too is multiplied by k? Or am I being incredibly dense, it does happen a lot

5. Oct 27, 2005

Beer-monster

Turn out the reason I was going wrong wasn't my method, I lost a minus in the calculation (slippery little blighters)

Thanks for the help anyway