- #1

maggie56

- 30

- 0

## Homework Statement

I have a pde,

16d

^{2}u/dxdy + du/dx + du/dy + au = 0 where a is constant.

## Homework Equations

## The Attempt at a Solution

I have tried to solve this pde using the substitutions x=e^t and y=e^s so t=ln(x) and s=ln(y) then finding

Du/dx= 1/x du/dt and du/dy= 1/y du/ds

For d

^{2}u/dxdy i am unsure if my answer is correct,

1/xy d

^{2}u/dsdt - 1/x du/dt - 1/y du/ds

When i substitute these into the pde i get 16/xy d

^{2}u/dsdt + au = 0

I could integrate this with respect to s and t but don't think that helps me.

Am i using the correct method here or is there a method that is better suited to my equation

Thank you for any help