Please show the work so that I may learn..... Using the Frobenius method, find a
ID: 1813477 • Letter: P
Question
Please show the work so that 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
B.) y1=(x- 1/3! x^3 + 1/5! X^5 - +-), y2=(1/x - x^2/2! + 1/4!x^4 - +-)