I have a 2nd order homogenous P.D.E:(adsbygoogle = window.adsbygoogle || []).push({});

(d^2)V/((dx)^2) + (d^2)V/((dy)^2) + 6(d^2)V/(dx dy) = 0

where all derivatives are partial derivatives. I need to transform this to form

a*(d^2)f/(dX^2) + b*(d^2)f/(dY^2) = 0 where a, b are constants and the derivatives are again partial, and f(X,Y) = V(x,y)

I I need to make a change of variables e.g x=cX +dY etc. but I get very messy algebraic expressions which I can't simplify. Thanks very much.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Partial differential equations: general solution

**Physics Forums | Science Articles, Homework Help, Discussion**