- #1
Fachni
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Homework Statement
Solve the following differential equations by series and also by an elementary method and verify that your solutions agree.
[tex](x^2+2x)y''-2(x+1)y'+2y=0[/tex]
Homework Equations
[tex]y=\sum_{n=0}^{\infty} a_nx^n[/tex]
[tex]y'=\sum_{n=1}^{\infty} na_nx^{n-1}[/tex]
[tex]y''=\sum_{n=1}^{\infty} n(n+1)a_{n+1}x^{n-1}[/tex]
The Attempt at a Solution
I have got [tex]a_1=a_0,\ a_3=0,\ a_4=-\frac{1}{8}a_3=0,\ a_5=-\frac{1}{5}a_4=0[/tex]. Then, how do we find the recursive relation to find the solution?
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