Find the recurrence relation an satisfies

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Reference no: EM132912228

Problem : INonautonomous ODE, Consider

x2y"(x) + xy' (x) - y(x) = 0, x > 0.

(a) This is a Cauchy-Euler equation. Find the general solution.

(b) Now, solve this problem with a power series centered at xo = 1, y(x) = Σ^∞_n=0a_n(x-1)ⁿ. Find the recurrence relation an satisfies.

(c) Taylor expand the two solutions you found in (a) at x₀ = 1. Check that the two series satisfy the recurrence relation you found in (b).

(d) In (c), one of the solutions is an infinite power series. What is the radius of convergence for that series?

Reference no: EM132912228

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