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3. Given the second-order, lincar, homogeneous differential cquation y" + 16y = 0 and the functions y1 (1) Y2(r) cos(4.r) sin(4.r) (a) Verify that yi(x) and y2(x) are solutions to the given differential equation.

3. Given the second-order, lincar, homogeneous differential cquation y" + 16y = 0 and the functions y1 (1) Y2(r) cos(4.r) sin(4.r) (a) Verify that yi(x) and y2(x) are solutions to the given differential equation.

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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I can do part a, but stuck on how to do b,c, and d.

3. Given the second-order, linear, homogeneous differential equation y" + 16y and the functions Y1(x) cos(4.r) = sin(4.x) Y2(x) (a) Verify that yı(x) and y2(x) are solutions to the given differential equation. (b) Verify that Yı(x) and y2(x) are linearly independent using the Wronskian. (c) yı (x) and y2(x) form a fundamental set of solutions to the linear, homogeneous differential equation. Find the general solution. (d) Let y(0) =1 and y'(0) = -2. Find the solution to the initial-value problem.
Transcribed Image Text:3. Given the second-order, linear, homogeneous differential equation y" + 16y and the functions Y1(x) cos(4.r) = sin(4.x) Y2(x) (a) Verify that yı(x) and y2(x) are solutions to the given differential equation. (b) Verify that Yı(x) and y2(x) are linearly independent using the Wronskian. (c) yı (x) and y2(x) form a fundamental set of solutions to the linear, homogeneous differential equation. Find the general solution. (d) Let y(0) =1 and y'(0) = -2. Find the solution to the initial-value problem.
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