The differential equation ay\" + by' + cy = f(t) hascharacteristic equation aλ2 + bλ + c = 0 whose roots are given ineach part below. The forcing function f(t) is also indicated.Sketch the form of the homogeneous solution to the differentialequation. Indicate the algebraic form of a particular solution.Sketch the form of the general solution for y(0) = y' (0) = 1.
(a) λ = −2, −3, f(t) = e −2t
(b) λ = −3, −3 (repeated real root), f(t) = sin(3t)
(c) λ = ±3i, f(t) = sin(2t)
(d) λ = ±3i, f(t) = sin(3t)
(e) λ = −2 ± 3i, f(t) = sin(3t)
