How to Solve a Partial Differential Equation with Variable Coefficients

[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

 

[mathmike]

http://www.calc101.com/

 

[HallsofIvy]

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

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.

 

[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

 

[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