Divide through by R:

We recognise this as a first order linear differential equation.

Identify P and Q:

Q = 0

Find the integrating factor (our independent variable is t and the dependent variable is i):

So

Now for the right hand integral of the 1st order linear solution:

Applying the linear first order formula:

Since i = V/R when t = 0:

Substituting this back in:

Solving for i gives us the required expression: