what are the benifits of laplace transformation and partial fractions in circuit analysis please

Question

mr.math · Answer

Most circuits that involve either a capacitor or an inductor or both have to be solved using a differential equation of some form, for example:
$\large \large \frac{d^2i}{dt}+\frac{R}{L}\frac{di}{dt}+\frac{1}{LC}i=0,$ with some initial conditions gives for $i(0)$ and $i'(0)$. One of the best tools (maybe the best) for solving such a differential equation is by using Laplace transform, or what you might call changing from "t-domain" to "s-domain".

mr.math · Answer

Partial fractions decomposition is  very important for you when you want to transform back your solution in s-domain to the t-domain.

mr.math · Answer

The numbers are not very nice. http://alturl.com/5cjad