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Variation of parameters. In the following exercises, two linearly independent solutions- y₁ and y2 —are given that satisfy the corresponding homogeneous equation. Use the method of variation of parameters to find a particular solution to the given non-homogeneous equation. Assume x > 0 in each exercise. (a) x² · y″ – 2y = 3x² − 1, y₁(x) = x², Y2(x) = x−¹. . (b) x² · y″ − (2a − 1)x · y′ + a² · y = xª+1, Y1 = xª,Y2 = xª ln(x).

Variation of parameters. In the following exercises, two linearly independent solutions- y₁ and y2 —are given that satisfy the corresponding homogeneous equation. Use the method of variation of parameters to find a particular solution to the given non-homogeneous equation. Assume x > 0 in each exercise. (a) x² · y″ – 2y = 3x² − 1, y₁(x) = x², Y2(x) = x−¹. . (b) x² · y″ − (2a − 1)x · y′ + a² · y = xª+1, Y1 = xª,Y2 = xª ln(x).

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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3. Variation of parameters. In the following exercises, two linearly independent solutions- y₁ and y2 -are given that satisfy the corresponding homogeneous equation. Use the method of variation of parameters to find a particular solution to the given non-homogeneous equation. Assume x > 0 in each exercise. (a) x² ⋅ y″ – 2y = 3x² − 1, y₁(x) = x², y2(x) = x¯¹. (b) x²-y" - (2a-1)x - y² + a² · y = xª+¹, Y₁ = xª,Y2 = xª ln(x).
Transcribed Image Text:3. Variation of parameters. In the following exercises, two linearly independent solutions- y₁ and y2 -are given that satisfy the corresponding homogeneous equation. Use the method of variation of parameters to find a particular solution to the given non-homogeneous equation. Assume x > 0 in each exercise. (a) x² ⋅ y″ – 2y = 3x² − 1, y₁(x) = x², y2(x) = x¯¹. (b) x²-y" - (2a-1)x - y² + a² · y = xª+¹, Y₁ = xª,Y2 = xª ln(x).
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