In this problem, y = c₁ cos(5x) + C₂ sin(5x) is a two-parameter family of solutions of the second-order DE y" + 25y = 0. If possible, find a solution of the differentialequation that satisfies the given side conditions. The conditions specified at two different points are called boundary conditions. (If not possible, enter NOT.)y(0) = 0, y(π/10) = 7y =Need Help?XRead Itatch It

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Answered: In this problem, y = c₁ cos(5x) + C₂…

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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Question

In this problem, y = c₁ cos(5x) + C₂ sin(5x) is a two-parameter family of solutions of the second-order DE y" + 25y = 0. If possible, find a solution of the differential
equation that satisfies the given side conditions. The conditions specified at two different points are called boundary conditions. (If not possible, enter NOT.)
y(0) = 0, y(π/10) = 7
y =
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Expert Solution

Step 1: Write the given differential equation

$Given space that space y equals c subscript 1 cos open parentheses 5 x close parentheses plus c subscript 2 sin open parentheses 5 x close parentheses space is space straight a space two space parameter space family space of space solutions space of space the space second space order space DE space y apostrophe apostrophe plus 25 y equals 0 Given space that space the space initial space conditions space space y open parentheses 0 close parentheses equals 0 space space comma space y open parentheses straight pi over 10 close parentheses equals 7$