Determine the unique solution of each of the following initial value problems: a) y" - 6y' + 25y = 0, y (0) = 5, y' (0) = 7. use the fact that y_h_1 (x) = e^3x cos (4x) and y_h_2 (x) = e^3x sin(4x) are solutions to the differential equation. b) x^2 y" - 4xy' + 6y = 0, y (1) = 4, y'(1) = 7. use the fact that y_h_1 (x) = x^2 and y_h_2 (x) = x^3 are solutions to the differential equation. c) y" - 2y' + y = 0, y (0) = 7, y'(0) = 4. use the fact that y_h_1 (x) = e^x and y_h_2 (x) = xe^x are solutions to the differential equation. y''' - 2y'' - y' + 2y = 0, y (0) = 0, y'(0) = 7, y"(0) = 3. use the fact that y_h_1 (x) = e^x, y_h_2 (x) = e^-x and y_h_2 (x) = e^2x are solutions to the differential equation.