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Let u₁ and u2 be two linearly independent solutions of the second-order linear differential equation (i) (ii) d²u dx² 2 fu + = Let w = u2/u1. Show that w' = c/u for some nonzero constant c. -2u1/u₁. Show that y satisfies the Ricatti equation Let y = y' - 0, ƒ = f (x). y² 2 - f.

Let u₁ and u2 be two linearly independent solutions of the second-order linear differential equation (i) (ii) d²u dx² 2 fu + = Let w = u2/u1. Show that w' = c/u for some nonzero constant c. -2u1/u₁. Show that y satisfies the Ricatti equation Let y = y' - 0, ƒ = f (x). y² 2 - f.

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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Let u₁ and u2 be two linearly independent solutions of the second-order linear differential equation (i) (ii) d² u fu dx² 2 + - 0, f = f(x). Let w = uz/u₁. Show that w' = c/u for some nonzero constant c. Let y = -2u₁/u₁. Show that y satisfies the Ricatti equation y² V-2-1 y' f.
Transcribed Image Text:Let u₁ and u2 be two linearly independent solutions of the second-order linear differential equation (i) (ii) d² u fu dx² 2 + - 0, f = f(x). Let w = uz/u₁. Show that w' = c/u for some nonzero constant c. Let y = -2u₁/u₁. Show that y satisfies the Ricatti equation y² V-2-1 y' f.
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