Let y = x and y = x2 be solutions of a differential equation P( x) y__ + Q( x) y_ + R(

Chapter 5, Problem 12

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QUESTION:

Let y = x and y = x2 be solutions of a differential equation P( x) y__ + Q( x) y_ + R( x) y = 0. Can you say whether the point x = 0 is an ordinary point or a singular point? Prove your answer. First-Order Equations. The series methods discussed in this section are directly applicable to the first-order linear differential equation P( x) y_ + Q( x) y = 0 at a point x0, if the function p = Q/ P has a Taylor series expansion about that point. Such a point is called an ordinary point, and further, the radius of convergence of the series y = _ n=0 an( x x0)n is at least as large as the radius of convergence of the series for Q/ P.

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QUESTION:

Let y = x and y = x2 be solutions of a differential equation P( x) y__ + Q( x) y_ + R( x) y = 0. Can you say whether the point x = 0 is an ordinary point or a singular point? Prove your answer. First-Order Equations. The series methods discussed in this section are directly applicable to the first-order linear differential equation P( x) y_ + Q( x) y = 0 at a point x0, if the function p = Q/ P has a Taylor series expansion about that point. Such a point is called an ordinary point, and further, the radius of convergence of the series y = _ n=0 an( x x0)n is at least as large as the radius of convergence of the series for Q/ P.

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