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Solve the following Differential Equations (a) (4D – 8D³ – 7D² + 11D +6)y = 0. Ans : y = ce-* + cze2r + €3e%z + c4e-= (b) (D³ +6D² + 12D + 8)y = 0, y(0) = 0, y(0) = 0, y"(0) = 2. Ans y = r'e-2z %3D %3D (c) y" + 6y" + 11ly + 6y = 0, y(0) = 0, y(0) = 1, y"(0) = -1. Ans y = 2e-- 3e-2 +e-3

Solve the following Differential Equations (a) (4D – 8D³ – 7D² + 11D +6)y = 0. Ans : y = ce-* + cze2r + €3e%z + c4e-= (b) (D³ +6D² + 12D + 8)y = 0, y(0) = 0, y(0) = 0, y"(0) = 2. Ans y = r'e-2z %3D %3D (c) y" + 6y" + 11ly + 6y = 0, y(0) = 0, y(0) = 1, y"(0) = -1. Ans y = 2e-- 3e-2 +e-3

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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1. Solve the following Differential Equations (a) (4D4-8D3 – 7D2 + 11D+6)y 0. Ans : y = cje- + cze2r + €3e3z + c4e- (b) (D3 + 6D² + 12D + 8)y = 0, y(0) = 0, y'(0) = 0, y"(0) = 2. Ans y = r'e-2x %3D %3D (c) y"+6y" +11y' + 6y 0, y(0) = 0, y'(0) = 1, y"(0) = -1. Ans y = 2e-I- 3e-2x + e-3r (d) y – 4y" + 14y" – 20y' + 25y = 0. Ans y = e" ((ci + Czx) cos(2r) + (cz + C42) sin(2x)) - %3D %3D
Transcribed Image Text:1. Solve the following Differential Equations (a) (4D4-8D3 – 7D2 + 11D+6)y 0. Ans : y = cje- + cze2r + €3e3z + c4e- (b) (D3 + 6D² + 12D + 8)y = 0, y(0) = 0, y'(0) = 0, y"(0) = 2. Ans y = r'e-2x %3D %3D (c) y"+6y" +11y' + 6y 0, y(0) = 0, y'(0) = 1, y"(0) = -1. Ans y = 2e-I- 3e-2x + e-3r (d) y – 4y" + 14y" – 20y' + 25y = 0. Ans y = e" ((ci + Czx) cos(2r) + (cz + C42) sin(2x)) - %3D %3D
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