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Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve the following ordinary differential equations using the power series method: (x-2) y' = 3y See the step by step example solutions in the picture .
Encc, 53 y'-y = 0 (C, + 2Cx + 3C,x + ..)- (C, + C,x + Cx? + ...) = 0 Collecting like powers of x: (C) - Co) + (2C, - C,)x + (3C, - C)x? + ... = 0 Then, C, - C, 0 C, = Co : 20- C, = 0 %3D 3C,- C, 0 C, = 3 2. C, = 3. C; = Therefore, y = C, + C, + C,x? + C,x' + .. y = C, + Cyx + C,x? + C+ x2 y = Co(l + x + 2! + ...) 3! y = Coe PROBLEM: I Solve the differential equation y" + y = 0 using the power series method. Tolu
Transcribed Image Text:Encc, 53 y'-y = 0 (C, + 2Cx + 3C,x + ..)- (C, + C,x + Cx? + ...) = 0 Collecting like powers of x: (C) - Co) + (2C, - C,)x + (3C, - C)x? + ... = 0 Then, C, - C, 0 C, = Co : 20- C, = 0 %3D 3C,- C, 0 C, = 3 2. C, = 3. C; = Therefore, y = C, + C, + C,x? + C,x' + .. y = C, + Cyx + C,x? + C+ x2 y = Co(l + x + 2! + ...) 3! y = Coe PROBLEM: I Solve the differential equation y" + y = 0 using the power series method. Tolu
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