Here is one more I am having a problem with:

[tex]4x^2y'' + 4xy' + (4x^2 - 1)y = 0, x > 0 [/tex]

one solution is

y

but when I try to work it all out with another linearly indep. solution

y

the order does not reduce and the y'' is huge... so I was wondering if I am missing some trick or is it really that painfully tedious

ps: couldn't figure out how to put x ^(-1/2) in latex

EDIT: I think I got it, but I did have to go through pages of writing out these derivatives.

[tex]4x^2y'' + 4xy' + (4x^2 - 1)y = 0, x > 0 [/tex]

one solution is

y

_{1}(x) = sin(x)* x^{-1/2}but when I try to work it all out with another linearly indep. solution

y

_{2}(x) = u(x) sin(x) * x^{-1/2}the order does not reduce and the y'' is huge... so I was wondering if I am missing some trick or is it really that painfully tedious

ps: couldn't figure out how to put x ^(-1/2) in latex

EDIT: I think I got it, but I did have to go through pages of writing out these derivatives.

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