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  3. the differential equation ay\" + by' + cy = f(t) h

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

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Advance Math

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)

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