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
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-> 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
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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):
(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
