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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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 16CR
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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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