Q: What is the solution of the equation d²y/dt² + y(t) = ∫₀ᵗ sinτ · y(t − π)dτ, subject to the initial conditions y(0) = 1 and (dy/dt)|_{t=0} = 0?
(a)y(t) = (1/2)(1 − cos√2t), for t > 0
(b)y(t) = (1/2)(1 + cos√2t), for t > 0
(c)y(t) = (1/2)(−1 − cos√2t), for t > 0
(d)y(t) = −(1/2)(1 − cos√2t), for t > 0
Correct Answer: (b)
Detailed explanation coming soon.