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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 (a) an equation with constant coefficients, (b) a Cauchy-Euler equation.

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 (a) an equation with constant coefficients, (b) a Cauchy-Euler equation.

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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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)
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