Find a basis of solutions by the frobenius method. Xy'' + 2y' + xy = 0

8) Use the method of Variation of Parameters to solve y" - y'= t. You - calculate determinants! can use MATHEMATICA to

X' = {(1, 2), (4, 3)} x X + {(8e3t), (12e2t)}. Where X1 = {(-e-t), (e-t)} and X2 = {(e5t), (2e5t)} are solutions of the corresponding homogeneous system. Show that the solutions of the corresponding homogeneous system are linearly independent. Find the fundamental matrix and its inverse. Solve the nonhomogeneous system given above. Show all of your work and multiply out all matrix calculations.