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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 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

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

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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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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