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**Differential equations and integral transforms**

Hi!

I have some general questions on using integral transforms for solving differential equations.

Also, I know that Fourier and Laplace transforms are useful means for solving linear ODE's and PDE's.

1. Are there cases, when one of them is more powerful as another one?

2. What about Hankel and Mellin transforms? Are there also very powerful?

3. I think, that Laplace transforms can be applied only for Cauchy problems (initial conditions must be given). Is it correct?

Thank you in advance

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