Approaching a Step Function Problem with Variation of Parameters

[seto6]

Homework Statement

Hello,

i have a small problem regarding this questions,

If the function vs(t) is a function for t>=0, i can solve thus no problem (we are required to solve using variation of parameters).

now i have a small problem, its not about how to solve it ,but how to approach this, it says let the vs(t) be a step function:

now, do i just let vs(t)=3t for time 0<=t<10, and solve this, and just ignore the time before 0, and then calculate for 0<=t<10 and t=>10, then add up the solution ?

Homework Equations

n/a

The Attempt at a Solution

If i did it from 0<=t<10 and t>10
for t>10, its just a homogeneous second order equation, that means the answer would be Vo(t)=2(homogeneous solution)+(particular solution, due to 3t).

any hints on how can i approach this problem, thank you very much in advance.

 

[vela]

Find solutions to the differential equation in each region and then join them smoothly at the boundaries. As you noted, for t>10, you have the homogeneous equation, so the solution in that region will be just the homogeneous solution.