Linear algebra question.

Please show all the steps.

5. (Soiving LTV systems ) Consider the time-varying differential equation .. 4. 2 y+;y+t2y=u(t) (l) for t > 0. Dene x1: y and x2 = j). (a) Write the system in the form 5dr) = A(t)x(t) + Bu(t). (2) (b) Assume 140') E 0 and nd two linearly independent solutions to the homogenous scalar system (I). (Hint: Try y = tk.) (0) Construct the matrix X0), a fundamental matrix for (2), using the results of part (b). ((1) Find the state-transition matrix (Mar)