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edr1c

  • 3 years ago

Solve the differential equation by means of power series about the ordinary point x=0. (1+x^2)y''-4xy'+6y=0

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  1. edr1c
    • 3 years ago
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    I'd found the recursion formula to be\[a _{m+2}=\frac{-(m-2)(m-3)a _{m}}{(m+2)(m+1)}\] from \[y=\sum_{m=0}^{\infty}a _{m}x ^{m}\] using \[a _{0},a _{1}\]as arbitary holders, my answer for m=2 onwards are 0, ie at m=2, \[a _{4}=0\] at m=3, \[a _{5}=0\] am i doing the question correctly?

  2. experimentX
    • 3 years ago
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    \[ a_2 = \frac{-6}{2} a_0 \\ a_3 = -\frac 2 6 a_1 \\ a_4 = ...\] I think at this point it's better to use software to find few terms

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