Question

I have two questions and if someone could help me out with these, that'd be great.

Suppose that r1 and r2 are the characteristic roots for ay double prime + by prime + cy = 0, so the solution is y(t) = c1e^r1t + c2e^r2t. For problem 34, discuss the long term solution behaviors for the given r1, r2 combinations. Assume beta doesn't equal 0.

34. r1 > 0, r2 < 0


36. Verify that e^(alpha t)cos beta t and e^(alpha t)sin beta t are linearly independent on any interval.