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Hi, so the problem is this:

I am trying to solve (analytically) the wave equation with c=1:

[tex]u_{xx}=u_{tt}[/tex]

on x,t>0 given the initial conditions

[tex]u(x,0)=u_{t}(x,0)=0, u(0,t)=sin(wt)[/tex]

I know how to solve on semi-infinite domains for quite a few cases using Green's Functions, Fourier Transforms, D'Alembert's solution and separation of variables. But I keep getting u=0 with these familiar methods due to the initial conditions of u being 0 and unmoving at t=0.

I feel like this is easier than I'm making it! Anyway, any help would be appreciated!

I am trying to solve (analytically) the wave equation with c=1:

[tex]u_{xx}=u_{tt}[/tex]

on x,t>0 given the initial conditions

[tex]u(x,0)=u_{t}(x,0)=0, u(0,t)=sin(wt)[/tex]

I know how to solve on semi-infinite domains for quite a few cases using Green's Functions, Fourier Transforms, D'Alembert's solution and separation of variables. But I keep getting u=0 with these familiar methods due to the initial conditions of u being 0 and unmoving at t=0.

I feel like this is easier than I'm making it! Anyway, any help would be appreciated!

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