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Verify that x = C₁ cost + C₂ sint is a two parameter family of solutions of the second-order DE x" + x = 0. Find a solution of the second-order IVP consisting of this differential equation and the initial conditions x(π/4) = √2, x' (π/4)2√2

Verify that x = C₁ cost + C₂ sint is a two parameter family of solutions of the second-order DE x" + x = 0. Find a solution of the second-order IVP consisting of this differential equation and the initial conditions x(π/4) = √2, x' (π/4)2√2

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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Verify that x = C₁ cost + C₂ sint is a two parameter family of solutions of the second-order DE x" + x = 0. Find a solution of the second-order IVP consisting of this differential equation and the initial conditions x(π/4) = √2, x' (π/4)2√2
Transcribed Image Text:Verify that x = C₁ cost + C₂ sint is a two parameter family of solutions of the second-order DE x" + x = 0. Find a solution of the second-order IVP consisting of this differential equation and the initial conditions x(π/4) = √2, x' (π/4)2√2
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