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.
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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Please answer question 1
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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