1) Consider the differential equation, y" + 4y = g(x). (a) Using the power series method, determine the solution of this

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1 Consider The Differential Equation Y 4y G X A Using The Power Series Method Determine The Solution Of This 1 (67.1 KiB) Viewed 49 times

1) Consider the differential equation, y" + 4y = g(x). (a) Using the power series method, determine the solution of this differential equation as a power series of the form Σo ªnx” for g(x) = 0. (12 points) (b) Using the power series method, determine the solution of this differential equation as a power series of the form o anx" for g(x) = 4x² +6. (4 points) 2) Starting from the series expansion for the Bessel function, ∞ (−1)n 2n+p Jp(x) = Σ (-)* T(n+1) T(n +1+p) n=0 prove the identity below. (16 points) Jp-1(x) — Jp+1(x) = 2Jp'(x)