Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am a mathematical physics student and I had the following question in my mind from few weeks. I couldn't find any solutions. I am very thankful to this site and I hope, I expect some good reasonable solution.

I would like to know the solution of equation in the form of:

$$\frac{\partial^2 w}{\partial t \partial x} = F\left(w, \frac{\partial w}{\partial t},\frac{\partial w}{\partial x}, \frac{\partial^2 w}{\partial t^2},\frac{\partial^2 w}{\partial^2 x}\right)$$

Please generalize by an example.

Thanks in advance.

as per the expert request I am giving a problem in the above form:

Find general solution of $$ \left(\frac{\partial w}{\partial x}\right)^2 \frac{\partial^2 w}{\partial t^2} = \left(\frac{\partial w}{\partial t}\right)^2 \frac{\partial^2 w}{\partial x^2}$$ and my second problem is $$2\frac{\partial w}{\partial t} \frac{\partial w}{\partial x}\frac{\partial^2 w}{\partial t\partial x} = \left(\frac{\partial w}{\partial x}\right)^2\frac{\partial^2 w}{\partial t^2} + \left(\frac{\partial w}{\partial t}\right)^2\frac{\partial^2 w}{\partial x^2}$$

Thanks in advance

share|cite|improve this question

migrated from Nov 13 '11 at 22:34

This question came from our site for active researchers, academics and students of physics.

This question is unanswerable as is. There is no way to give the solution to an unspecified equation. What equation are you interested in? – Ron Maimon Nov 12 '11 at 23:10
Now I added the problems. Plz answer... – dr.jgk Nov 13 '11 at 16:36

I don't know if it's possible to give more general solutions, but for your first equation, there are solutions of the following forms: $$ w(x,t) = F(a x + b t)$$ and $$ w(x,t) = F((x + a)(t + b)) $$ where $a,b$ are arbitrary constants and $F$ is an arbitrary $C^2$ function. For your second equations, there are solutions of the following forms: $$ w(x,t) = F(a x + b t)$$ and $$ w(x,t) = F((x+a)/(t + b))$$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.