Suppose we are given y₁) and y2(x) (with y₁ ‡ y2), which are two different solutions of a nonhomogeneous equation y" + xy = x². (1) Write down a linear second order, which is satisfied by u = y₁ - 3y2.
Suppose we are given y₁) and y2(x) (with y₁ ‡ y2), which are two different solutions of a nonhomogeneous equation y" + xy = x². (1) Write down a linear second order, which is satisfied by u = y₁ - 3y2.
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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![**Nonhomogeneous Differential Equations**
Suppose we are given \(y_1(x)\) and \(y_2(x)\) (with \(y_1 \neq y_2\)), which are two different solutions of a nonhomogeneous equation
\[ y'' + xy = x^2. \tag{1} \]
Write down a linear second order, which is satisfied by \(u = y_1 - 3y_2\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b031bca-7361-4239-8354-1517112b98e0%2F4b732cce-49f9-4e4b-8bfc-7688be2892f2%2F9k13k1b_processed.png&w=3840&q=75)
Transcribed Image Text:**Nonhomogeneous Differential Equations**
Suppose we are given \(y_1(x)\) and \(y_2(x)\) (with \(y_1 \neq y_2\)), which are two different solutions of a nonhomogeneous equation
\[ y'' + xy = x^2. \tag{1} \]
Write down a linear second order, which is satisfied by \(u = y_1 - 3y_2\).
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