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MATH 325 ODE - Coggle Diagram
MATH 325 ODE
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Series Solutions
Ordinary Points
Let \( y = \sum_{n=0}^{\infty} a_n x^n\), substitute it into L[y]
Require \(L[y] = y''+p(x)y'+q(x)y \): p(x), q(x) analytic
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Regular Singular Points
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General Solution: \( |x-x_0|^r\sum_{n=0}^{\infty} a_n (x-x_0)^n \) or let \(x>x_0, a_0=1\) then \( y=(x-x_0)^r[1+\sum_{n=1}^{\infty} a_n (x-x_0)^{n}] \)
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