Consider the solution of x³y" + 3x² y' -15x y = h x^b+1 (x0) ,

h > 0 and b is a constant parameter to be determined.

a) Find a proper value of h , such that the variable x can be chosen from - to with x 0 , avoid the solution of y = c x , and make the solution y = y(x) remain real valued?

b) By choosing proper values of b, you may obtain pairs of real-valued solutions, check if they are LI.

c) If x = 1, we have y(1) = 0 and y'(1) = 6, determine your final solution.

d) Check the stability of the solution, list the unstable conditions.