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Given $3u_{tt} + 10u_{xt} + 3u_{xx} = \sin(x+t)$ find the general solution.

I have yet to solve any inhomogeneous second order PDE (or even first order ones at that). For homogeneous PDE of same order, I managed to solve them by factoring the operators and so forth. Being new to PDEs (self studying via Strauss PDE book) I lack the intuition to find a clever way of solving these, however from my experience with ODEs I reckon there is a way to solve these by first solving the associated homogeneous first by factoring operators and so forth and stuff.. but not finding much progress on incorporating the $\sin(x+t)$ term.

Any help & direction to solving this would be greatly appreciated.

  • 0
    Did you try to change the coordinates? For example, write $u(t,x)=v(\phi(t,x))$ where $\phi$ is a linear bijective transformation such that $3u_{tt}+10u_{xt}+3u_{xx}$ is simpler.2011-09-30
  • 0
    I tried but failed to find a suitable candidate for the change as the $sin(x+t)$ and the various partial terms were throwing me off (It was easily doable in first order but second order adds more to take into factor)2011-09-30
  • 0
    Put $u(t,x)=v(at+bx,x)$. The partial derivatives are simpler.2011-09-30

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