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+ 4. In each case, find a second order, linear, homogeneous ODE that has the given pair of functions as its solutions. Then show that the pair forms a fundamental set of solutions. (a) y₁ = 2e³t - 5e-t, y₂ = 11e-t (b) y₁ = cos(πt), y₂ = sin(nt) Y2 (c) y₁ = e²t cos(5t), y2 = e²t sin(5t) (d) y₁ = e³t, y₂ = te³t

+ 4. In each case, find a second order, linear, homogeneous ODE that has the given pair of functions as its solutions. Then show that the pair forms a fundamental set of solutions. (a) y₁ = 2e³t - 5e-t, y₂ = 11e-t (b) y₁ = cos(πt), y₂ = sin(nt) Y2 (c) y₁ = e²t cos(5t), y2 = e²t sin(5t) (d) y₁ = e³t, y₂ = te³t

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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4. Please solve the following differential equation.

4. In each case, find a second order, linear, homogeneous ODE that has the given pair of functions as its solutions. Then show that the pair forms a fundamental set of solutions. (a) y₁ = 2e³t - 5e-t, y2 = (b) yı sin(t) (c) y₁ = e²t cos(5t), y₂ = e²t sin(5t) (d) y₁ = e³t, y2 = te³t = cos(πt), y₂ = 11e-t =
Transcribed Image Text:4. In each case, find a second order, linear, homogeneous ODE that has the given pair of functions as its solutions. Then show that the pair forms a fundamental set of solutions. (a) y₁ = 2e³t - 5e-t, y2 = (b) yı sin(t) (c) y₁ = e²t cos(5t), y₂ = e²t sin(5t) (d) y₁ = e³t, y2 = te³t = cos(πt), y₂ = 11e-t =
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