In: Advanced Math
Suppose y1 = -6e3t - 6t2 and y2 = 4e-2t - 6t2 are both solutions of a certain nonhomogeneous equation: y'' + by' + cy = g(t).
a. Is y = 12e3t - 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.