dy dx (²), y(a)= A. (a) Show that by introducing the new dependent variable v(x) by the relation y = xv, equation (3.14) is transformed to the separable form = dv dx Use this transformation to find solutions of the following equations. = F(v) X - V v(a) = 41. a 2 (3.14)
dy dx (²), y(a)= A. (a) Show that by introducing the new dependent variable v(x) by the relation y = xv, equation (3.14) is transformed to the separable form = dv dx Use this transformation to find solutions of the following equations. = F(v) X - V v(a) = 41. a 2 (3.14)
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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Question

Transcribed Image Text:dy
dx
= F (²)
(²), y(a)= A.
by the relation y
(a) Show that by introducing the new dependent variable v(x)
xv, equation (3.14) is transformed to the separable form
=
dv
dx
Use this transformation to find solutions of the following equations.
F(v) — v
9
X
v(a)
=
(3.14)
A
a
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