I missed the day of class where we went over solving 2nd order diff-eqs.
y''(t) - 100 y(t) = 0
subject to y(0)=100 and y'(0)=3000
Thank you!
This is second order linear constant coefficient homogeneous.
So the characteristic equation is
.
So the solution is
.
You have two initial conditions: and .
From the first, we can see
.
From the second...
.
So now you have two equations in two unknowns:
.
Adding them together, we find
.
Back substituting:
.
So finally, the solution is
.