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

[Maximtopsecret]

Homework Statement

u_t − 2u_x =1/ u;
what expressions are constant along the equations's characteristics?

Homework Equations

3. The Attempt at a Solution [/B]
Am I right?
dt=dx/(-2)=du/(-1/u), -2t=x=u²;
u=sqrt(x); u=sqrt(-2t) are constant.

 

[MarcusAgrippa]

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

 

[Maximtopsecret]

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

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

 

[MarcusAgrippa]

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

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.