most recent 30 from http://mathoverflow.net 2013-06-18T21:04:22Z http://mathoverflow.net/feeds/question/52091 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/52091/inhomogeneous-wave-equation-solution thenickname 2011-01-14T17:04:20Z 2011-01-14T18:33:49Z

<p>(<strong>Edit</strong>: <a href="http://math.stackexchange.com/questions/17505/inhomogeneous-wave-equation-solution" rel="nofollow">Reposted at Math.SE</a> )</p> <p>Psi_xx - Psi_tt - 4Psi = exp(exp(3it))*dirac_delta(x) DE valid for all x,t (no boundary conditions specified). Solve for Psi. If the DE is singular, then nontrivial solutions are okay.</p> <p>-I solved the homogeneous portion, Psi_homogeneous, of this equation via separation of variables but my solution is just for some random case of k^2 where: F''/F = G''/G + 4 = k^2. I chose the case where k^2 = 0 which gave me solutions for Psi_homogeneous like x*sin((4^0.5)*t) and x*cos((4^0.5)*t).</p> <p>-With the guess method for Psi_particular, I have no idea what to guess on a general form of exp(exp(3it))*dirac_delta(x) to plug back in to the PDE.</p> <p>-I have read about Green's Functions but, man, I'm having a hard time understanding the guides I have seen because they skip so many of the intermediate steps. I understand that these Green's Functions can provide a general solution and that seems like what I'm looking for. I likely spent a lot of time for nothing on my first attempt with separation of variables for Psi_homogeneous and then looking for Psi_particular using the guess method...</p> <p>-I'm curious if there is a general set of IC/BCs that I should be assuming as well? </p>