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By variation of parameters, solve y" +4y= sin²x. Hint: You will have to apply some trigonometric identities to determine parameters u₁ and u₂.

By variation of parameters, solve y" +4y= sin²x. Hint: You will have to apply some trigonometric identities to determine parameters u₁ and u₂.

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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dy 1. Solve (D2 + 3D - 4)²(D² - 2D + 1)³(D² + 7)y = 0, Dy dx 2. Determine the form of the particular solution, yp for the differential equation: y(4) +9y" = (x² + 1) sin 3x Note: You may used the concept of annihilator. 3. Determine the form of the particular solution, y, for the differential equation: (D - 1)³(D² - 4)y = xe + e²x + e-* Note: You may used the concept of annihilator. 4. By method of undetermined coefficients, solve: y(4) − y(³) — y" — y' – 2y = 8x³. 5. By variation of parameters, solve y" +4y= sin²x. Hint: You will have to apply some trigonometric identities to determine parameters u₁ and u₂.
Transcribed Image Text:dy 1. Solve (D2 + 3D - 4)²(D² - 2D + 1)³(D² + 7)y = 0, Dy dx 2. Determine the form of the particular solution, yp for the differential equation: y(4) +9y" = (x² + 1) sin 3x Note: You may used the concept of annihilator. 3. Determine the form of the particular solution, y, for the differential equation: (D - 1)³(D² - 4)y = xe + e²x + e-* Note: You may used the concept of annihilator. 4. By method of undetermined coefficients, solve: y(4) − y(³) — y" — y' – 2y = 8x³. 5. By variation of parameters, solve y" +4y= sin²x. Hint: You will have to apply some trigonometric identities to determine parameters u₁ and u₂.
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