Question

I need help on partial differential equations. How to solve them?

Answer 1

Solving them in general is a huge topic. Much better if you ask us a specific question.

Answer 2

\[\delta ^{2}u / \delta ^{2}x +\delta ^{2}u/ \delta x \delta y +\delta ^{2}u / \delta ^{2}y = y \cos x\]

Answer 3

This is a linear, inhomogeneous equation. The way the usually think about tackling this sort of equation is completely analogous to the ordinary differential equation (ODE) problem: find the homogeneous solution, then find the particular solution.

Now, to find either of those solutions, you'll want to think about using a trial solution/Ansatz of the form

u(x,y) = X(x)Y(y).

Substitute this into the differential equation and reduce it to ODEs.

Answer 4

If this is a problem for your course, I'm sure you're not getting this cold. Go back and look at the examples you have seen to date in your lectures or in the text book.

Answer 5

Thanks!