Please show the work so I may learn..... Using the Frobenius method, find a basi

Question

Please show the work so I may learn.....

Using the Frobenius method, find a basis of solutions of the ODE:
                                                    x^2y''+4xy'-(x^2-2)y=0                                                                           

A.)    y1= (1-(1/2)x^2 + 9/56x^4 -+...), y2=(1/x - x^2 + 9/2 x^4 - +-)

B.)   y1=(x- 1/3! x^3 + 1/5! X^5 - +-), y2=(1/x - x^2/2! + 1/4!x^4 - +-)

C.)    y1= (1/x + X/6 + 1/120 x^3 + 1/5040 X^5 + -), y2=(1/x^2 + 1/2 + 1/24 X^2 + 1/720 x^4+-)

D.)    y1=(1/x^2 - 2/3x^2 + 2/15x^2 - 4/315x^4 + -...), y2=(1/x^3 - 2/x^2 + 2/3x - 4/45x^3 + -..)                                              

E.)    None of the above; see Problem Work

Explanation / Answer

option C

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