Short-answer question on characteristics of p.d.e

1. May 26, 2015

Maximtopsecret

1. The problem statement, all variables and given/known data
ut − 2ux =1/ u;
what expressions are constant along the equations's characteristics?
2. Relevant equations
3. The attempt at a solution

Am I right?
dt=dx/(-2)=du/(-1/u), -2t=x=u2;
u=sqrt(x); u=sqrt(-2t) are constant.

2. Jun 1, 2015

MarcusAgrippa

I think that they may want a slightly more general answer. Have you quoted the question precisely as it was stated?

3. Jun 1, 2015

Maximtopsecret

Oh yes, the question is stated just like there...

4. Jun 2, 2015

MarcusAgrippa

Then, apart from the fact that you have ignored the second branch of the square root function, your answer is correct. It may be better to quote the solution function u(x,t) in implicit form rather than to solve it explicitly for u. That way you include both branches of the square root function.