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.
Thats because the differential equation has variable coefficients, so one gets a differential equation of s. I've seen other exercises likes this. Perhaps I wasn't clear, the function I'm looking is y(t), y(s) denotes it's Laplace transform.
When I apply the laplace transform on the equation I get:
Then using
And
I get for example:
I don't know y'(0), but its a constant, then when deriving I get to the second equation that I put at the beginning.