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6. (a) Verify that the functions x1 = e²t and x2 = e-2t are solutions of the that x3 = x₁ + x2 and linear differential equation " - 4x = 0. Verify x4 = 10x1 are solutions as well. (c)-(2)

6. (a) Verify that the functions x1 = e²t and x2 = e-2t are solutions of the that x3 = x₁ + x2 and linear differential equation " - 4x = 0. Verify x4 = 10x1 are solutions as well. (c)-(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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6. (a) Verify that the functions x1 = e²t and x2 = e-2t are solutions of the linear differential equation x" - 4x = 0. Verify that x3 = x₁ + x2 and 4 = 10x1 are solutions as well. 201 1 1 are solutions of t t +1 (b) Verify that the functions x₁ = and x₂ = the nonlinear differential equation x" + 2xx' = 0, but x3 = x₁ + x2 and X4 = = 10x₁ are not.
Transcribed Image Text:6. (a) Verify that the functions x1 = e²t and x2 = e-2t are solutions of the linear differential equation x" - 4x = 0. Verify that x3 = x₁ + x2 and 4 = 10x1 are solutions as well. 201 1 1 are solutions of t t +1 (b) Verify that the functions x₁ = and x₂ = the nonlinear differential equation x" + 2xx' = 0, but x3 = x₁ + x2 and X4 = = 10x₁ are not.
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