# Series Solutions of Second Order Linear Equations : Ordinary Point, General Solution, Power Series and Radius of Convergence

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Verify that x0=0 is an ordinary point of the differential equation:

y''+ xy' + 2y = 0

Find two linearly independent solutions to the differential equation in the form of a power series about x0=0. If possible, find the general term in each solution. Write the general solution

Verify that x0=0 is an ordinary point for the differential equation:

....

Find the first four terms of the power series of two linearly independent solutions. Estimate the lower bound for the radius of convergence of the two solutions.

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Ordinary Point, General Solution, Power Series and Radius of Convergence are investigated. The solution is detailed and well presented.

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Problem #1

. Let , , then we have . In this form, when , and are finite. So is an ordinary point.

Now assume that is in the form of power series. Then we ...

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