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Find a general solution to the second order differential equation using variation of parameters. You may use the fact that ye = C₁ cos(2t) + C₂sin (2t) y" + 4y = csc (2t)

Find a general solution to the second order differential equation using variation of parameters. You may use the fact that ye = C₁ cos(2t) + C₂sin (2t) y" + 4y = csc (2t)

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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5. Find a general solution to the second order differential equation using variation of parameters. You may use the fact that y = C₁ cos(2t) + C₂sin (2t) y" + 4y = csc (2t) Laplace Transforms you may find helpful for later problems: Function Laplace Transform 1 eat cos (ax sin (ax) tn ect cos (at) ect sin (at) u(t), unit step function uc (t)f(t-c) for some arbitrary function f(t) y" S 1 S. 1 S a s² + a² a s² + a² n! gn+1 S + C (s + c)² + a² (s + c)² + a² ecs ecs F(s) SY-y(0) s2Y-sy(0)-y'(0)
Transcribed Image Text:5. Find a general solution to the second order differential equation using variation of parameters. You may use the fact that y = C₁ cos(2t) + C₂sin (2t) y" + 4y = csc (2t) Laplace Transforms you may find helpful for later problems: Function Laplace Transform 1 eat cos (ax sin (ax) tn ect cos (at) ect sin (at) u(t), unit step function uc (t)f(t-c) for some arbitrary function f(t) y" S 1 S. 1 S a s² + a² a s² + a² n! gn+1 S + C (s + c)² + a² (s + c)² + a² ecs ecs F(s) SY-y(0) s2Y-sy(0)-y'(0)
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