You are solving a 2x2 system of the form : PỸ + where P has constant entries with real different eigenvalues. s(t) = Decide which of the following statements is correct: I can find a particular solution using the undetermined coefficients method with a try function of the form Y(t) = sin(t)ā + cos I can find a particular solution using the undetermined coefficients method with a try function of the form Y(t) = (cos(t) + sin(t))ä I can only find the general solution for this problems using the Variation of Parameters method. Undetermined Coefficients won't work in this case. I can find the general solution using the undetermined coefficients method. To find the particular solution I should use a with a try function of the form Y(t) = sin(t)ā

Please show step-by-step solution and do not skip steps. Explain your entire process in great detail. Explain how you reached the answer you did.

(2 cos 2t / 19. Assume that a real 2 x 2 matrix A has an eigenvalue of A1 = 3+ 2i with a corresponding eigenvector = (6) Find the general solution of the system of differential equations 2i given by 글 %=D Az. cos 2t sin 2t 교(t) = cie3t ( sin 2t + cze³t 2 cos 2t cos 2t sin 2t a(t) = c1e3t + cze3t -2 sin 2t 2 cos 2t (. cos 2t sin 2t a(t) Ciešt + cze3t sin 2t - cos 2t ( -2 cos 2t sin 2t a(t) = cie3t + cze3t sin 2t -2 cos 2t cos 2t ( 2 sin 2t ) sin 2t a(t) = c1e3t + cze³t 2 cos 2t

This is the first part of a two-part problem. Let P=[-: 1 5₁(t) = [(41) 5₂(t) = - sin(4t). a. Show that y₁ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix product y(t) = = 0 [1] -4 Enter your answers in terms of the variable t. -4 sin(4t) -4 cos(4t)] ÿ₁ (t) [181-18] b. Show that y₂ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix product Enter your answers in terms of the variable t. 04] 32(t) = [-28]|2(t) 181-181