I have a wave equation Ytt=c^2 Yxx - g where g is a constant. The boundary conditions are Y(0,t)=Y(L,t)=0 with initial conditions Y(x,0)=0 and Yt(x,0)=0 I tried to solve it by Laplace transfoming the PDE in time and everything worked fine until I got to the point where I had to inverse the transform but things got ugly. Obviously, I have a nonhomogenous PDE with homogeneous boundary conditions. I was going to expand everything in terms of the related eigenfunctions sin(n Pi x/L)but it's not right to expand the constant g in terms of eigenfunctions. I can't do seperation of variables because the PDE is inhomogeneous. What's the trick here to get me started without using integral transforms?(adsbygoogle = window.adsbygoogle || []).push({});

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# 1D wave equation with gravity

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