The Attempt at a Solution
Write the KCL equation
Do the derivation to get rid of the integral, replace all possibly values, we got:
solve A(s)=s2+10s+25=0, we got the natural response in(t)=A1+A2.e-5t
Replace the inductor with a short circuit, the capacitor with open circuit, so I have ip=0
and the initial condition i(0+)=i(0-)=0. (**)
So the solution should be i(t)=in+ip
I thought I was wrong at (**) and maybe at (*) cause the vs' would be zero and the solution would be zero as well.