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4. Given the solution y₁(x) to the five homogeneous linear ODEs listed below, use reduction of order to find a second solution to these ODES: (a) y" - 4y + 4y = 0, Y₁ = e²x; (b) (1 — 2x − x²)y" + 2(1 + x)y′ − 2y = 0, (c) xy"+y' = 0 Y₁ = ln x; Y₁ = x + 1;

4. Given the solution y₁(x) to the five homogeneous linear ODEs listed below, use reduction of order to find a second solution to these ODES: (a) y" - 4y + 4y = 0, Y₁ = e²x; (b) (1 — 2x − x²)y" + 2(1 + x)y′ − 2y = 0, (c) xy"+y' = 0 Y₁ = ln x; Y₁ = x + 1;

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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4. Given the solution y₁(x) to the five homogeneous linear ODEs listed below, use reduction of order to find a second solution to these ODES: 2x Y₁ = e²x; (a) y" - 4y + 4y = 0, (b) (1 – 2x − x²)y" + 2(1+x)y' - 2y = 0, (c) xy" + y = 0 Y₁ = ln x; Yı Y₁ = x + 1;
Transcribed Image Text:4. Given the solution y₁(x) to the five homogeneous linear ODEs listed below, use reduction of order to find a second solution to these ODES: 2x Y₁ = e²x; (a) y" - 4y + 4y = 0, (b) (1 – 2x − x²)y" + 2(1+x)y' - 2y = 0, (c) xy" + y = 0 Y₁ = ln x; Yı Y₁ = x + 1;
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