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I stuck with method of characteristics here, how to find the general solution and IVP?

${u_{xx} + 4u_{xy}+3u_{yy}}={0}, -\infty <x<+\infty, t >0 $

$ u(x,0)=0, -\infty <x<+\infty, $

$ u_y(x,0)=x^2, -\infty <x<+\infty,$

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closed as off-topic by John Omielan, RRL, Wrzlprmft, Cesareo, José Carlos Santos Mar 9 at 14:17

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  • $\begingroup$ You can also do this problem by noting that the transformation: $$\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} 1 & 1 \\ 1 & 3 \end{bmatrix}\begin{bmatrix} \xi \\ \eta \end{bmatrix}$$ Converts your PDE to the form: $$u_{\xi \eta}=0$$ $\endgroup$ – projectilemotion Mar 9 at 8:47