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x² + ²x + (1 - 1) = 4x 16. ₁(x) = x ¹2 sin x y₂(x) = x-¹/2 cos x -1/2

x² + ²x + (1 - 1) = 4x 16. ₁(x) = x ¹2 sin x y₂(x) = x-¹/2 cos x -1/2

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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HELP 16, please show the work

For Problems 13-17, find a particular solution of the nonhomogeneous equation, given that the functions y(x) and y₂(x) are linearly independent solutions of the corresponding homogeneous equation. Note: The coefficient of y" must always be 1, and hence a preliminary division may be required. x²y" - 2xy + 2y = x² sin x 13. yı(x) = x Y₂(x) = x² x²y" + xy' - 4y = 14. y₁(x) = x² (1-x)y" + xy' - y = 2(x - 1)² e-* Y₂(x) = et 15. yı(x) = x J" + -y' + + (1 - 1) x(x + x³) y₂(x) = x=2 y" - y =e-x* -12 16. ₁(x) = x¹2 sin x y₂(x) = x12 cos x X 17. yı(x) = e* y = x-1/2 y₂(x)= ex
Transcribed Image Text:For Problems 13-17, find a particular solution of the nonhomogeneous equation, given that the functions y(x) and y₂(x) are linearly independent solutions of the corresponding homogeneous equation. Note: The coefficient of y" must always be 1, and hence a preliminary division may be required. x²y" - 2xy + 2y = x² sin x 13. yı(x) = x Y₂(x) = x² x²y" + xy' - 4y = 14. y₁(x) = x² (1-x)y" + xy' - y = 2(x - 1)² e-* Y₂(x) = et 15. yı(x) = x J" + -y' + + (1 - 1) x(x + x³) y₂(x) = x=2 y" - y =e-x* -12 16. ₁(x) = x¹2 sin x y₂(x) = x12 cos x X 17. yı(x) = e* y = x-1/2 y₂(x)= ex
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