- #1
Miriverite
- 6
- 0
[solved] solutions to Laplace's equation
Find all solutions f(x,y) that satify Laplace's equation that are of the form:
ax^3 + bx^2y + cxy^2 + dy^3
Laplace states that fxx + fyy = 0
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?
Homework Statement
Find all solutions f(x,y) that satify Laplace's equation that are of the form:
ax^3 + bx^2y + cxy^2 + dy^3
Homework Equations
Laplace states that fxx + fyy = 0
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?
Last edited: