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In Exercises 59 and 60, two linearly independent solutions y₁ and y2 are given to the associated homogeneous equation of the variable- coefficient nonhomogeneous equation. Use the method of variation of parameters to find a particular solution to the nonhomogeneous equa- tion. Assume x > 0 in each exercise. 59. x²y" + 2xy' - 2y = x², y₁ = x², y₁ = x 60. x²y" + xy' - y = x, y₁ = x¯¹, y2 = x

In Exercises 59 and 60, two linearly independent solutions y₁ and y2 are given to the associated homogeneous equation of the variable- coefficient nonhomogeneous equation. Use the method of variation of parameters to find a particular solution to the nonhomogeneous equa- tion. Assume x > 0 in each exercise. 59. x²y" + 2xy' - 2y = x², y₁ = x², y₁ = x 60. x²y" + xy' - y = x, y₁ = x¯¹, y2 = x

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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In Exercises 59 and 60, two linearly independent solutions y₁ and y2 are given to the associated homogeneous equation of the variable- coefficient nonhomogeneous equation. Use the method of variation of parameters to find a particular solution to the nonhomogeneous equa- tion. Assume x > 0 in each exercise. 59. x²y" + 2xy' - 2y = x², y₁ = x², y₁ = x 60. x²y" + xy' - y = x, y₁ = x¯¹, y2 = x
Transcribed Image Text:In Exercises 59 and 60, two linearly independent solutions y₁ and y2 are given to the associated homogeneous equation of the variable- coefficient nonhomogeneous equation. Use the method of variation of parameters to find a particular solution to the nonhomogeneous equa- tion. Assume x > 0 in each exercise. 59. x²y" + 2xy' - 2y = x², y₁ = x², y₁ = x 60. x²y" + xy' - y = x, y₁ = x¯¹, y2 = x
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