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I need to solve this ODE using the laplace transform:

y" + y - exp (-t^2) = 0 , y(0) = y'(0) = 0

My question is on how to find the laplace transform of exp (-t^2).

I used different properties of laplace transform to solve it but I was not succesfull. I was thinking that I can find the laplace transform of exp (-t^2) by a simple transformation of u = -t^2 and then using the derivative property of laplace transform. But it didn't work.

I really appreciate any helps to solve this problem.

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# Homework Help: Laplace transform of exp (-t^2)

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