Using Scientific Notebook, we can solve it in one step.

We set up a matrix with the differential equation and initial conditions:

`(d^2i)/(dt^2)+2(di)/(dt)=u(t-10)-u(t-20)`

` i(0)=0`

`i^(\ ')(0)=0`

Exact solution is:

`i(t)=-e^(-2t)/4{-2 "Heaviside"(t-10)te^(2t)` `+21e^(2t) "Heaviside"(t-10)` `+2 "Heaviside"(t-20)te^(2t)` `-41e^(2t) "Heaviside"(t-20)` `-"Heaviside"(t-10)e^(20)` `+"Heaviside"(t-20)e^(40))}`

NOTE: SNB 's inbuilt unit step function is called the "Heaviside" function. So when it produces an answer, it is in terms of "Heaviside".

This simplifies to:

`i(t)=1/4((2t-21+e^(-2t+20))*u(t-10)` `-(2t-41+e^(-2t+40))*u(t-20))`