Find a general formula for the coefficient an in a power

Chapter 8, Problem 4RP

(choose chapter or problem)

Find a general formula for the coefficient $a_{n}$ in a power series expansion about $x=0$ for a general solution to the given equation.

(a) $\left(1-x^{2}\right) y^{\prime \prime}+x y^{\prime}+3 y=0$

(b) $\left(x^{2}-2\right) y^{\prime \prime}+3 y=0$

Equation Transcription:

${a}_{n}$

$x=0$

$(1-{x}^{2})y''+xy'+3y=0$

$({x}^{2}-2)y''+3y=0$

Text Transcription:

x=0

(1-x2)y''+xy'+3y=0

(x2-2)y''+3y=0

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