Consider the initial value problem a. Form the complementary solution to the homogeneous equation. ýc(t) = C₁ ýp(t) - el et y₁(t) Y₂(t) 0 LJ+ -6 sin t+2 cos t 8 sin t + C₂ b. Construct a particular solution by assuming the form ÿp(t) = de²t + bt + c and solving for the undetermined constant vectors a, b, and c. et 7(0) = [H]. c. Form the general solution y(t) = c(t) + yp(t) and impose the initial condition to obtain the solution of the initial value problem. 2e¹10e¹-6 sin t+2 cos t -4e¹ + 10e + 8 sin t

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