Solving for x ? [differential equation]
I'm stuck with this equation and I can't figure out a way how to solve for t..
So I got the solution of a differential equation(complex roots), and now I need to find the values of t for which y=3.5
3.5 = 12e^(-αt)*cos(ω t) - 12α/ω*e^(-αt)*sin(ω t)
α and ω are constants, I tried changing it to the exponential form, cosine form but it didn't help.
In fact what I need is the time intervals for which y(t) > 3.5
Any tips or advice how to do it ?