Solving LaPlace Equation for x^3?
Good evening everyone! I have a little bit of a headache from trying to figure out how to attack this complex analysis problem:
(2nd partial derivative of u with respect to y)+(2nd partial derivative of u with respect to x)=x^3
(Laplace's equation on the left, x^3 on the right). We are supposed to find u. Now, Our teacher's hint was this:
4*d/dz*du/d(z-bar) is equivalent to LaPlace's equation.
My thinking was this: Integration by parts should suffice from there. But, I have hit a huge mental block-- I cannot seen to get x^3 in terms of z. That would make this all go through a lot better. Do any of you guys have any suggestions? I would love to hear any of them! Thanks so much!
PS (I was thinking of just using my diffeq knowledge and stating that u could be equal to 1/20(x^5)+cx+dy+e*xy+f, but I couldn't help but feel that would be cheating...)