We start with:


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):

`intP\ dt=int1/(RC)dt` `=1/(RC)t`



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

`intQe^(intPdt)dt=int0\ dt=K`

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:


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