Hi there. I have to solve the differential equation using the laplace transform.

So, applying the Laplace transform on both sides of the equality, and using some properties of the Laplace transform I get:

Then:

Then I have to apply the inverse transform to get the function I'm looking for, but the thing is I don't know the inverse Laplace transform for the arctangent of s. I think I have probably done something wrong, but I couldn't find the mistake.