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- What is the criteria for a given differential equation to be solvable using Laplace transform?

Hi,

I was trying to see if the following differential equation could be solved using Laplace transform; its solution is y=x^4/16.

You can see below that I'm not able to proceed because I don't know the Laplace pair of xy^(1/2).

Is it possible to solve the above equation using Laplace transform? In my opinion, I don't think so.

Thank you.

I was trying to see if the following differential equation could be solved using Laplace transform; its solution is y=x^4/16.

You can see below that I'm not able to proceed because I don't know the Laplace pair of xy^(1/2).

Is it possible to solve the above equation using Laplace transform? In my opinion, I don't think so.

Thank you.