Ac Transient analysis of RC series circuit

[Sriman Dutta]

Hi!

I was trying to analyse the RC series circuit for a sinusoidal AC input. I fed the input with an AC voltage V1sin(wt), and found the differential equation for the voltage across the capacitance Vo. 

RC dVo/dt +Vo = V1sin(wt)

I assumed the capacitor was chargeless, so Vo = 0 at t=0. 

Next I tried to solve for Vo using two methods. I used Laplace transform and brute-force solving the differential equation itself. 

However I arrived at two different results, considering the same initial condition. 

 

Please see if I'm missing something. Or do give an explanation. I know it's very trivial, but this is getting on my nerves. 

 

PS: I didn't know the right category for this question so posted under Engineering. 

I am so sorry. It was a mistake. Please take back the post. 

[Enthalpy]

Both must give the same answer. I agree with your equation, if the input connects to R and the output across C.

Once the transient has vanished, are the outputs computed by both methods identical? Then the error lies in the initial value and its effect.

Don't invest more time in transient responses than your exams need. I'm the one guy from the whole engineering school who made circuitry after the diploma, but I never needed anything refined from the >300h course I got about circuit analysis, systems and so on.