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(6 pts) Consider the second order linear differential equation a. Solve the diff

ID: 2870038 • Letter: #

Question

(6 pts) Consider the second order linear differential equation a. Solve the differential equation. Use A and B to denote arbitrary constants and t the independent variable. b. Write the differential equation as an equivalent first order system using the substitution y(t) = x'(t) . c. For the matrix from part (b), find the eigenvalues and the corresponding eigenvectors. Fill in all the blanks before submitting. The eigenvalue lambda 1 = corresponds to the eigenvector v1 = The eigenvalue lambda 2 = corresponds to the eigenvector v2 = d. Find the real-valued general solution to the system in part (b). Use A and B to denote arbitrary constants and t the independent variable. e. How does the solution you found in part (d) compared to the one in part (a)?

Explanation / Answer

a) x(t) =Ae^(-4t)*sin(2t) + Be^(-4t)*cos(2t)

b) We can write higher order differential equations as a system with a very simple change of variable. We