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1. (LI-3) Consider the following nonhomogeneous equation: x²y" - 2xy' + 2y = 4x². We can find one solution to the associated homogeneous equation r²y" - 2xy + 2y = 0 to be y₁ = x. Use this solution along with reduction of order to find the full general solution of the nonhomogeneous equation. (Note: The parameters of the general solution will be the constants of integration you get when you solve for u.)

1. (LI-3) Consider the following nonhomogeneous equation: x²y" - 2xy' + 2y = 4x². We can find one solution to the associated homogeneous equation r²y" - 2xy + 2y = 0 to be y₁ = x. Use this solution along with reduction of order to find the full general solution of the nonhomogeneous equation. (Note: The parameters of the general solution will be the constants of integration you get when you solve for u.)

Advanced Engineering Mathematics
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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**1. Consider the following nonhomogeneous equation:** \[ x^2 y'' - 2xy' + 2y = 4x^2. \] We can find one solution to the associated homogeneous equation \( x^2 y'' - 2xy' + 2y = 0 \) to be \( y_1 = x \). Use this solution along with reduction of order to find the full general solution of the nonhomogeneous equation. *(Note: The parameters of the general solution will be the constants of integration you get when you solve for \( u \).)*
Transcribed Image Text:**1. Consider the following nonhomogeneous equation:** \[ x^2 y'' - 2xy' + 2y = 4x^2. \] We can find one solution to the associated homogeneous equation \( x^2 y'' - 2xy' + 2y = 0 \) to be \( y_1 = x \). Use this solution along with reduction of order to find the full general solution of the nonhomogeneous equation. *(Note: The parameters of the general solution will be the constants of integration you get when you solve for \( u \).)*
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We use reduction of order to find other solution and then we find particular solution.

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