I have a pde,
16d2u/dxdy + du/dx + du/dy + au = 0 where a is constant.
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 d2u/dxdy i am unsure if my answer is correct,
1/xy d2u/dsdt - 1/x du/dt - 1/y du/ds
When i substitute these into the pde i get 16/xy d2u/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