u(adsbygoogle = window.adsbygoogle || []).push({}); _{xx}- x^{2}u_{yy}= 0 (assume x>0)

Is there any systematic method (e.g. change of variables) to solve this hyperbolic equation?

dy/dx = [B + sqrt(B^{2}- AC)]/A

=> dy/dx = x

=> 2y -x^{2}= c

dy/dx = [B - sqrt(B^{2}- AC)]/A

=> dy/dx = -x

=> 2y + x^{2}= k

So the characteristic curves are 2y -x^{2}= c and 2y + x^{2}= k

Now does this imply that the general solution is u = f(2y-x^{2})+g(2y+x^{2}) ?

Thanks!

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# 2nd order linear hyperbolic PDE?

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