Show that y = uv with v(x) = exp (-1/2 ∫ p(x) dx) gives from the ODE y + p(x)y' + q(x)y = 0 the ODE u + [q(x) - 1/4p(x) 2 - 1/2p' (x)] u = 0, not containing the first derivative of u.

Chapter 5, PROBLEM SET 5.4 #16

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Show that y = uv with v(x) = exp (-1/2 ∫ p(x) dx) gives from the ODE y" + p(x)y' + q(x)y = 0 the ODE

u" + [q(x) - 1/4p(x)- 1/2p' (x)] u = 0,

not containing the first derivative of u.

Related Book For answer-question

Advanced Engineering Mathematics

10th edition

Authors: Erwin Kreyszig

ISBN: 978-0470458365