**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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Answered: Suppose we are given y₁) and y2(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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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.