Use power series method to solve the differential equation y(0) = 1, y'(0) = 0, y" + 2xy + 2y = 0, by following the step

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Use Power Series Method To Solve The Differential Equation Y 0 1 Y 0 0 Y 2xy 2y 0 By Following The Step 1 (31.27 KiB) Viewed 66 times

Use power series method to solve the differential equation y(0) = 1, y'(0) = 0, y" + 2xy + 2y = 0, by following the steps below. (a) If y(x) = -0 Cna" is the solution to the above initial value problem, then write down the recurrence relation satisfied by the cn's. (b) Write down the coefficients Co, C2, C4, C6, Cs and C₁, C3, C5, C7 and then write down the general form of c2n and C2n+1 by looking at the pattern. c) Can you write the infinite series solution in terms of the exponential function?