# Easy DE

1. Oct 5, 2008

### kasse

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

Find the solution of the equation

uxy = ux

3. The attempt at a solution

ux = p

py = p

ln p = y + c*

p = ce^y

But them, what is u?

Last edited: Oct 5, 2008
2. Oct 5, 2008

### HallsofIvy

Staff Emeritus
Well, how would you solve the ORDINARY differential equation. dp/dx= p? That's seems to me very easy. Warning: because this is NOT an ordinary differential equation, the "constant" in the solution may be a function of y. Also remember that the general solution to a partial differential equation involves unknown FUNCTIONS.

3. Oct 5, 2008

### kasse

Just integrate wrt. x so that

u(x,y) = e^y Int[c(x)]dx + g(y) where c(x) and g(y) are arbitrary?