2 6. [15] For the diffelentia] equation x2 dy+x y = X (but2 dx a. Make the usual variable substitution, x = et to restructure this equation as a differential equation with constant coefficients with respect to the variable t. Show all work! b. Solve the resultant homogenous (a function of t) part of the equation in a. \"the easy way\" as a second order differential equation with constant coefficients. Next c. Solve for the particular solution in terms of the variable t using variation of parameters. d. Write the entire solution y(t) to the inhomogeneous differential equation in the variable t (from parts b and c) and then as a function of the variable x, that is y(x). e. Write the solution in part d. as a function of X for the following initial conditions \"3:0, [13100 = 2] dx 7. (6 continued) [10] f. Assuming a series solution resolve the homogenous equation solved in part 6.b above. g. Comment on the solutions found in parts 7f with respect to a Taylor series expansions of the solution found in part 6b above. h. [Extra credit 10] Solve for the particular solution in part c. above using the Green's function =0 t=U approach. Make the boundary condition in this case y(0) = 0, y'(t]