2 For each of the following cases, find the condition such that the Wronskian W[y1, 92] = 0. For arbitrary y(x), calculate the 3 x 3 Wronskian W[y₁, 92, y]. Write down the differential equation which results from setting W[y1, 92, y] verify that y₁, y2 are solutions of this differential equation. (a) yı = eλ₁x, y2 = - (b) y₁ = x¹, y2 = x^². = e¹₂x₁ = 0 and

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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2 For each of the following cases, find the condition such that the Wronskian W[y₁, 92] #
0.
For arbitrary y(x), calculate the 3 × 3 Wronskian W[y₁, 92, y].
Write down the differential equation which results from setting W[y₁, 92, Y]
verify that y₁, y2 are solutions of this differential equation.
= еx₁x₂ , Y2 = e¹2x
(a) y₁ =
(b) y₁ = x¹, y2 =
= x^².
= 0 and
Transcribed Image Text:2 For each of the following cases, find the condition such that the Wronskian W[y₁, 92] # 0. For arbitrary y(x), calculate the 3 × 3 Wronskian W[y₁, 92, y]. Write down the differential equation which results from setting W[y₁, 92, Y] verify that y₁, y2 are solutions of this differential equation. = еx₁x₂ , Y2 = e¹2x (a) y₁ = (b) y₁ = x¹, y2 = = x^². = 0 and
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