hello is anybody can solve this question from advanced mathematics?

8. Find the well-behaved solution (i.e., u(x) -> 0 as x -> too ) of this DE 5.1 du do 2 + ( 28 - x2 ) u (x) = 0 and the eigenvalues, &, following the steps below: a, Substitute u (x) = exp(-x2/2) h(x) to get a DE for h (x). b. Find a series solution for h(x). c. Find the condition on the eigenvalues, &, for the series h ( x ) to be a finite polynomial. d. How does the series behave for (x >> 1 if it does not terminate? HINT: Compare ratios of coefficients you find to corresponding ratios of coefficients in one of the Series below for indices n> > 1. e. For cases of finite series, find the second and third order polynomials h (x)