SOLUTION: {{{(x^2 + 2) d^2y/dx^2 + 3x dy/dx - y = 0}}} (tried to write this as simply (x^2 + 2)y'' + 3xy' - y = 0 but it would not let me use the apostrophe in the formula so had to re-wr

Question 1048333:
(tried to write this as simply (x^2 + 2)y'' + 3xy' - y = 0 but it would not let me use the apostrophe in the formula so had to re-write it , came out a bit ugly but i hope you understand it)
Find two linearly independent solutions around x=0.
Now I know this is a second order linear differential equation, but all the examples I can find usually write a question based on only constants, not variables.
e.g 3y'' + 2y' + y = 0
Since my question has x and y, how do I deal with that? :(
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

(x^2 + 2)y" + 3xy' - y = 0

is good enough.  This involves the Sturm-Liouville theory
and the Legrangian to get a closed solution.

That gets too advanced for this site.  You might try for

a Frobenius series solution.  This video might help you do that:

https://www.youtube.com/watch?v=Gq7MxHjtAdw

Edwin

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