Let u₁ and u2 be two linearly independent solutions of the second-orderlinear differential equation(i)(ii)d² ufudx² 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 equationy²V-2-1y'f.

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Answered: Let u₁ and u2 be two linearly…

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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Which differential equation follows the form ?
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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.