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2. Use an appropriate method to find the general solution of the following differential equat (a) y" + 3y' – 2y = -e2" (5 cos 2x + 9 sin 2a)

2. Use an appropriate method to find the general solution of the following differential equat (a) y" + 3y' – 2y = -e2" (5 cos 2x + 9 sin 2a)

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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Pls answer question 2 

1. Suppose m = {0,0,0, 1, –5, 4±3i, 4±3i} are roots of an auxiliary equation. Write down the general solution of the corresponding homogeneous linear DE if it is (а) an equation with constant coefficients, (b) a Cauchy-Euler equation. 2. Use an appropriate method to find the general solution of the following differential equations: (a) y" + 3y' – 2y = -e2" (5 cos 2x + 9 sin 2x) (b) x?y" + 15xy' + 58y = 0 (c) y" – y = 1- e-2r (d) y" – 6y" + 11y' – 6y = e2" (5 – 4x – 32²)
Transcribed Image Text:1. Suppose m = {0,0,0, 1, –5, 4±3i, 4±3i} are roots of an auxiliary equation. Write down the general solution of the corresponding homogeneous linear DE if it is (а) an equation with constant coefficients, (b) a Cauchy-Euler equation. 2. Use an appropriate method to find the general solution of the following differential equations: (a) y" + 3y' – 2y = -e2" (5 cos 2x + 9 sin 2x) (b) x?y" + 15xy' + 58y = 0 (c) y" – y = 1- e-2r (d) y" – 6y" + 11y' – 6y = e2" (5 – 4x – 32²)
2. Use an appropriate method to find the general solution of the following differential equations: / – 2y = -e2" (5 cos 2x + 9 sin 2x) 2 (b) x?y" + 15xy' + 58y = 0 (c) y" – - y = 1-e-2r (d) y" – 6y" + 11y – 6y = e2" (5 – 4x – 32²) - 3. Solve the following differential equation subject to the indicated conditions. y" – y = x + sin x, y(0) = 1, y'(0) = -3
Transcribed Image Text:2. Use an appropriate method to find the general solution of the following differential equations: / – 2y = -e2" (5 cos 2x + 9 sin 2x) 2 (b) x?y" + 15xy' + 58y = 0 (c) y" – - y = 1-e-2r (d) y" – 6y" + 11y – 6y = e2" (5 – 4x – 32²) - 3. Solve the following differential equation subject to the indicated conditions. y" – y = x + sin x, y(0) = 1, y'(0) = -3
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