2. (a) Show that the substitution v ln y transforms the differential equation Q(x) (y In y), yP(x)y into the linear equation o'- Q(x)v = -P(x) (b) Use this substitution to solve the differential equation ry' -4xy2y In y = 0. 3. Consider the initial value nroblem

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question
2. (a) Show that the substitution v
ln y transforms the differential equation
Q(x) (y In y),
yP(x)y
into the linear equation
o'- Q(x)v = -P(x)
(b) Use this substitution to solve the differential equation
ry' -4xy2y In y = 0.
3. Consider the initial value nroblem
Transcribed Image Text:2. (a) Show that the substitution v ln y transforms the differential equation Q(x) (y In y), yP(x)y into the linear equation o'- Q(x)v = -P(x) (b) Use this substitution to solve the differential equation ry' -4xy2y In y = 0. 3. Consider the initial value nroblem
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