The auxiliary equation for our differential equation is:
A.E. `m^2-4m+4` `=(m-2)^2` `=0`
In this case, we have:
`m=2` (repeated root)
We need to use the second form from the table above (`y = e^(mx)(A + Bx)`), and once again use the correct variables (t and s, instead of x and y).
Now to find the values of the constants:
`s(0)=1` implies `A=1`
So we can write
`s'(0)=3 ` implies `2+B=3`
This gives us `B=1`
The graph of our solution is as follows:
Graph of displacement `s(t)=(1+t)e^(2t)`.