I need help with solving this equation, please.
In an RLC circuit, L =1H, C = 1/5F, R =2Ohm and f(t) = 2 sin t. Write down the differential equation that describes v(t), the voltage across capacitor, and solve it with initial conditions v(0) = 0 and dv(0)/dt = 3. Ans = - cos t + 2 sin t + e^(-t) (cos 2t + sin 2t)
So far I've managed to obtain the equation of V(s) = [F(s) + 3LC] / [LC s^2 +RCs + 1 ]
RC = 2/5
LC = 1/5
F(s) = 1 /(s^2 + 1)
V(s) = [(1/(s^2 + 1)) + 3/5] / [(1/5)s^2 + (2/5)s + 1]
I tried to solve it by doing partial equation but ended up with wrong answers.