The indicated function y₁(x) is a solution of the associated homogeneous equation. y" - 5y' + 4y = x; Let y = u(x)y₁ and w(x) = u'(x). Use the method of reduction of order to find a second solution y₂(x) of the homogeneous equation and a particular solution y(x) of the given nonhomogeneous equation. Find the integrating factor of the associated linear first-order equation in w(x). eSP(x) dx = Find the derivative u '(x). Find y₂(x) and y(x). Y₂(x) = 3 5 4 16 Y₁ = ² X
The indicated function y₁(x) is a solution of the associated homogeneous equation. y" - 5y' + 4y = x; Let y = u(x)y₁ and w(x) = u'(x). Use the method of reduction of order to find a second solution y₂(x) of the homogeneous equation and a particular solution y(x) of the given nonhomogeneous equation. Find the integrating factor of the associated linear first-order equation in w(x). eSP(x) dx = Find the derivative u '(x). Find y₂(x) and y(x). Y₂(x) = 3 5 4 16 Y₁ = ² X
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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Transcribed Image Text:The indicated function y₁(x) is a solution of the associated homogeneous equation.
y" 5y + 4y = x;
Let y = u(x)y₁ and w(x) = u'(x).
Use the method of reduction of order to find a second solution y₂(x) of the homogeneous equation and a particular solution y(x) of the given nonhomogeneous equation.
Find the integrating factor of the associated linear first-order equation in w(x).
= JP(x)dxے
Find the derivative u '(x).
Find y₂(x) and y(x).
Y₂(x) =
Yp(x) =
3
4
5
16
X
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