Question

For problems 3-6, note that if y(t) is a solution of the homogeneous problem, then y(t−t0) is a solution as well, where t0 is a fixed constant. So, for example, the general solution of a problem with complex roots can be expressed as y(x) = c1e µ(t−t0) cos(ω(t − t0)) + c1e µ(t−t0) sin(ω(t − t0)) When initial conditions are given at time t = t0 and not t = 0, expressing the general solution in terms of t − t0 will result in simpler equations for the constants c1 and c2.

2y'' + y' − 10y = 0, y(1) = 5, y' (1) = 2.

Answer 1