Answer to Question #159960 in Differential Equations for kashif ali

Question

what is method of finding the solution of the 2nd order partial differential equations by using laplace transform method?

Answer 1

 The first step in using Laplace transforms to solve an IVP is to take the transform of every term in the differential equation by Using the appropriate formulas of Laplace transforms.

Then Plug in the initial conditions and collect all the terms that have a Y

At this point it’s convenient to recall just what we’re trying to do. We are trying to find the solution to an IVP. What we’ve managed to find at this point is not the solution, but its Laplace transform. So, in order to find the solution all that we need to do is to solve the partial fraction then finally take the inverse transform.