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**[solved] solutions to Laplace's equation**

**1. The problem statement, all variables and given/known data**

Find all solutions f(x,y) that satify Laplace's equation that are of the form:

ax^3 + bx^2y + cxy^2 + dy^3

**2. Relevant equations**

Laplace states that fxx + fyy = 0

**3. The attempt at a solution**

fxx = 6ax + 2by

fyy = 6dy + 2cx

so 6ax + 2by + 6dy + 2cx = 0

(3a+c)x + (3d+b)y = 0

What do I do from here?

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