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Let U1 and U2 be two linearly independent solutions of the second-order linear differential equation d²u fu + dx² 2 - y' Let w= uz/u1. Let y=-2u₁/u₁. ,2 0, f = f(x). 2 = f. (iii) Show that w"/w' = - 2u₁/u₁, and deduce that w satisfies the equation 2 1 ()'. () - () - 2 = f.

Let U1 and U2 be two linearly independent solutions of the second-order linear differential equation d²u fu + dx² 2 - y' Let w= uz/u1. Let y=-2u₁/u₁. ,2 0, f = f(x). 2 = f. (iii) Show that w"/w' = - 2u₁/u₁, and deduce that w satisfies the equation 2 1 ()'. () - () - 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 d²u dx² + fu 2 y' - Let w= u2/01. Let y = -2u₁/u₁. :0, f= f(x). y² 2 = f. (iii) Show that w" /w' = −2u₁/u₁, and deduce that w satisfies the equation 1 2 ()' - () - s. = f. W² 2
Transcribed Image Text:Let U1 and U2 be two linearly independent solutions of the second-order linear differential equation d²u dx² + fu 2 y' - Let w= u2/01. Let y = -2u₁/u₁. :0, f= f(x). y² 2 = f. (iii) Show that w" /w' = −2u₁/u₁, and deduce that w satisfies the equation 1 2 ()' - () - s. = f. W² 2
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