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Problem 1 Suppose that y1, y2 are solutions to a homogeneous second-order linear differential equation. Which of the following pairs of y₁ and y2 are linearly independent: (a) y₁ = 9 - 6x, y2 = 10x - 15 ☐ 1 (b) y₁=-4sin3x, y2 = 5 cos 3.x (c) y₁= 3e4r Y2 = e-2x 1 (d) y₁=2 sin² x, y2 = -1 + cos² a E Check the box(es) with linearly independent functions. Explain you answers.

Problem 1 Suppose that y1, y2 are solutions to a homogeneous second-order linear differential equation. Which of the following pairs of y₁ and y2 are linearly independent: (a) y₁ = 9 - 6x, y2 = 10x - 15 ☐ 1 (b) y₁=-4sin3x, y2 = 5 cos 3.x (c) y₁= 3e4r Y2 = e-2x 1 (d) y₁=2 sin² x, y2 = -1 + cos² a E Check the box(es) with linearly independent functions. Explain you answers.

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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Problem 1 Suppose that y₁, y2 are solutions to a homogeneous second-order linear differential equation. Which of the following pairs of y₁ and y2 are linearly independent: (a) y₁=9-6x, y2 = 10x15 (b) y₁=-4sin3x, y2 = 5 cos 3x (c) y₁ = 3e4 -2x Y2 = e (d) y₁ = 2 sin² x, y₂ = -1 + cos²x Check the box(es) with linearly independent functions. Explain you answers. 50000
Transcribed Image Text:Problem 1 Suppose that y₁, y2 are solutions to a homogeneous second-order linear differential equation. Which of the following pairs of y₁ and y2 are linearly independent: (a) y₁=9-6x, y2 = 10x15 (b) y₁=-4sin3x, y2 = 5 cos 3x (c) y₁ = 3e4 -2x Y2 = e (d) y₁ = 2 sin² x, y₂ = -1 + cos²x Check the box(es) with linearly independent functions. Explain you answers. 50000
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