Consider the differential equation (x2 + 1) y" + 4xy = 0.
(a) Without solving, if y(x) =
an xn is used to solve this differential equation, is it possible to predict (with 100% certainty) that the
solution will be a general solution? If yes, find the open interval of convergence of the general solution. If no, explain why the solution is
not a general solution.
(b) Use y(x) =
an xn to solve this differential equation. Write your solution in sigma notation and simplify as much as possible.
This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.