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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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i need solutions for this tyy
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ffbc1d8-30c0-4fb7-b8ef-40672e1fb1c7%2Fb33919d7-7a5e-4b7e-9d7a-0f90acb96702%2Fvbt6vxm_processed.jpeg&w=3840&q=75)
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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