Suppose y1 = -6e3t - 6t2 and y2 = 4e-2t - 6t2 are both solutions of...

Suppose y₁ = -6e^3t - 6t² and y₂ = 4e^-2t - 6t² are both solutions of a certain nonhomogeneous equation: y'' + by' + cy = g(t).

a. Is y = 12e^3t - 4e^-2t + 6t² also a solution of the equation?

b. Is y = -6t² also a solution of the equation?

c. Could any constant function y = c also be a solution? If so, find all possible c.

d. What is the general solution of the equation?

e. Determine the coefficients b, c, and g(t) in the equation above.

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Expert Solution

Colby Messinger answered 1 year ago

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