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anonymous
 one year ago
Due Tomorrow, and it's 1:30 in the morning.
Given the Linear ODE y''xy'+2y=0
(a). Find two linearly independent power series solutions of this equation.
(b). What is the radius of convergence of these series?
anonymous
 one year ago
Due Tomorrow, and it's 1:30 in the morning. Given the Linear ODE y''xy'+2y=0 (a). Find two linearly independent power series solutions of this equation. (b). What is the radius of convergence of these series?

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freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[y(x)=\sum_{n=0}^\infty a_n x^n \\ y'(x)=\sum_{n=1}^\infty n a_n x^{n1} \\ y''(x)=\sum_{n=2}^\infty n(n1)a_nx^{n2} \\ \sum_{n=2}^\infty n(n1)a_nx^{n2}x \sum_{n=1}^{\infty} na_nx^{n1}+2 \sum_{n=0}^{\infty} a_nx^n=0 \\ \\ \sum_{n=0}^\infty (n+2)(n+1)a_{n+2}x^{n} \sum_{n=1}^{\infty}na_{n}x^{n}+2 \sum_{n=0}^\infty a_nx^n=0 \\ \\ \\ \] \[2(1)a_2+2a_0+\sum_{n=1}^\infty[ (n+2)(n+1)a_{n+2}x^{n}na_nx^{n}+2a_nx^{n}]=0 \\ \\ 2a_2+2a_0+\sum_{n=1}^{\infty} x^n[(n+2)(n+1)a_{n+2}n a_n+2 a_n]=0 \\ \] maybe you can going from here
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