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If your DEs are linear, you can use Laplace transforms to find an exact solution. This is much simpler than inexact numerical methods.
by dreamcompiler 6y ago
If your DEs are linear, you can use Laplace transforms to find an exact solution. This is much simpler than inexact numerical methods.
- btrettel 6y agoNot quite. The Laplace transform only works for constant coefficient linear equations as far as I'm aware. And it is inappropriate for many boundary value problems, because it solves a problem over a domain from 0 to infinity when that might not be what you want. With this being said, I'm a big fan of integral transforms in general (Fourier and Laplace particularly) and have used them many times to solve both ODEs and PDEs.