Consider the partial dierential equation, (y(adsbygoogle = window.adsbygoogle || []).push({}); ^{4}-x^{2})u_{xx}- 2xyu_{xy}- y^{2}u_{yy}= 1. We will make the substitution x = s^{2}- t^{2}and y = s - t, to simplify

(a) Solve for s and t as functions of x and y

the farthest point i got to was

x = s^2 - t^2 = (s+t)(s-t) = y(s+t)

y = s - t

s+t = x/y

i don't know what to do after that.. i have the solution, but i have no idea how to get to it.

the solution is

s = x + y^2 / 2y

t = x - y^2 / 2x

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# Higher order partial derivatives

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