Solution of RC Circuit first order differential equation

 

Hi here is me with new Problem "How to calculate the i(t) of RC series circuit by using laplace of first order differential equation" It was very hard to calculate for first time for undergraduates and very short forms written in book so look here.

Here is circuit:

1. Switch on at time t=0 then the initial condition at capacitor is nill means 0.

by KVL:

in function of t

Apply Laplace Transform

as we write before that initial condition at C is zero

then manipulate till end solution

Now apply Inverse Laplace 

Inverse Laplace formula

We get this 

Thanks 

If you have any question then comment me