A power series solution y=sum_ n=0 ^infty a_n x^n to an ODE converges in a neighbourhood of an ordinary point x_0 up to the distance to the nearest:

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CSS Applied Mathematics QUESTION #1333

Question 1

A power series solution \(y=\sum_{n=0}^\infty a_n x^n\) to an ODE converges in a neighbourhood of an ordinary point \(x_0\) up to the distance to the nearest:

Irregular singular point
Singular point✔️
Ordinary point
Boundary point

Correct Answer Explanation

By the theorem on power series solutions, if \(x_0\) is an ordinary point of the ODE, the power series solution converges in the interval \(|x-x_0|

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