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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)

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)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(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 2a) (b) x²y" + 15xy' + 58y = 0 4e-* (c) y" – : - y = 1 – e-2x (d) y" – 6y" + 11y' – 6y = e2" (5 – 4r – 3r?) 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:(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 2a) (b) x²y" + 15xy' + 58y = 0 4e-* (c) y" – : - y = 1 – e-2x (d) y" – 6y" + 11y' – 6y = e2" (5 – 4r – 3r?) 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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