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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8bff41aa-0e32-4db1-8ef9-ff3703c241e8%2F9dc81ee9-b2b9-4f67-8061-4fef9c9bfb47%2Fjqvzz5_processed.jpeg&w=3840&q=75)
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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