# Help with basic pde

1. Sep 21, 2008

### jomomma

http://mathbin.net/906 [Broken]

cant figure this one out

Last edited by a moderator: May 3, 2017
2. Sep 21, 2008

### tiny-tim

Welcome to PF!

Hi jomomma! Welcome to PF!

(type "tex" instead of "EQ" on this forum )

What have you tried?

3. Sep 21, 2008

### HallsofIvy

What do you mean by "figure this out"? Did you stare at it expecting the answer to suddenly pop into your head or did you DO something like writing down the equations of the characteristics?

If the latter, please show us what you did!

4. Sep 21, 2008

### jomomma

I tried doin characteristics but i am getting confused with the $$u_z$$ term. Heres what i do

$$$\frac{dx}{dt}&=&x\Rightarrow x=x_0e^t$ $\frac{dy}{dt}&=&2y\Rightarrow y=y_0e^2t$ $\frac{dz}{dt}&=&1\Rightarrow z=z_0 + t$ $\frac{du}{dt}&=&3u\Rightarrow u=u_0e^3t$$$

from there i try to put $$y$$ and $$x$$ in to the equation for $$u$$

$$u=xy=x_0y_0e^3t$$

what do i do with $$z$$ and $$\varphi(x,y)$$

Last edited: Sep 21, 2008
5. Sep 23, 2008

### jomomma

could someone verify whether the correct answer is

$$u(x,y,z)=\varphi(xe^{-z},ye^{-2z})e^{3z}$$

6. Sep 23, 2008

### NoMoreExams

Can't you plug it in and check like you would with any DE?

7. Sep 23, 2008

### jomomma

yes, i can and i have, but i wanted third party confirmation, because i may not have included all solutions or may have made a mistake