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In this problem, verify that the given functions y₁ and y2 satisfy the corresponding homogeneous equation. Then find a particular solution of the nonhomogeneous equation that does not involve any terms from the homogeneous solution. x²y" - 3xy + 4y = 19x² ln x, x > 0, y₁(x) = x², y₂(x) = x² ln x. NOTE: Enter an exact answer. (x) = 19 22 (la(s)); (ln(x))³ 6

In this problem, verify that the given functions y₁ and y2 satisfy the corresponding homogeneous equation. Then find a particular solution of the nonhomogeneous equation that does not involve any terms from the homogeneous solution. x²y" - 3xy + 4y = 19x² ln x, x > 0, y₁(x) = x², y₂(x) = x² ln x. NOTE: Enter an exact answer. (x) = 19 22 (la(s)); (ln(x))³ 6

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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In this problem, verify that the given functions y₁ and y2 satisfy the corresponding homogeneous equation. Then find a particular solution of the nonhomogeneous equation that does not involve any terms from the homogeneous solution. x²y" − 3xy' + 4y = 19x² ln x, x > 0, y₁(x) = x², y2(x) = x² ln x. NOTE: Enter an exact answer. 19 Y(x) = x² (ln(x))³ 6
Transcribed Image Text:In this problem, verify that the given functions y₁ and y2 satisfy the corresponding homogeneous equation. Then find a particular solution of the nonhomogeneous equation that does not involve any terms from the homogeneous solution. x²y" − 3xy' + 4y = 19x² ln x, x > 0, y₁(x) = x², y2(x) = x² ln x. NOTE: Enter an exact answer. 19 Y(x) = x² (ln(x))³ 6
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