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I was wondering if anyone could give me a hand with this initial value problem.

It s to be solved via Laplace transform.

y''(x)-xy'(x)+y(x)=5 , y(0)=5 and y'(0)=3

Applying the transform to the given equation I end up to :

sY'(s)+(s^2+2)Y(s)=5/s^2 + 5s + 3

This is a non linear first order differential equation with the variable s.

Any ideas to continue?

Thanks in advance!!!