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I Solution of an ODE in series Frobenius method

  1. Dec 23, 2016 #1
    Hi
    I am supposed to find solution of $$xy''+y'+xy=0$$
    but i am left with reversing this equation.
    i am studying solution of a differential equation by series now and I cannot reverse a series in the form of:
    $$ J(x)=1-\frac{1}{x^2} +\frac{3x^4}{32} - \frac{5x^6}{576} ....$$

    $$ \frac{1}{J}=1+\frac{x^2}{2} +\frac{5x^4}{32}+ \frac{23x^6}{576}...$$

    General formula of $J(x)$ is $$\sum_{n=0}^{\infty} \frac{(-1)n}{(n!)^2}(\frac{x}{2})^2$$

    Thanks for all help!!
     
  2. jcsd
  3. Dec 24, 2016 #2

    ShayanJ

    User Avatar
    Gold Member

    Why do you need to reverse it?
     
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