The differential equation ay" + by' + cy = f(t) has characteristic equation aλ2 + bλ...

The differential equation ay" + by' + cy = f(t) has characteristic equation aλ2 + bλ + c = 0 whose roots are given in each part below. The forcing function f(t) is also indicated. Sketch the form of the homogeneous solution to the differential equation. 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)

(d) λ = ±3i, f(t) = sin(3t)

(e) λ = −2 ± 3i, f(t) = sin(3t)

Solutions

Expert Solution

Colby Messinger answered 10 months ago

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