Given the ordinary differential equation dy da = a) Show that it is invariant under the GTPL y²+(x2x2)y 2³ - x(x + y) - (x + €)y x = x + €, y = I b) Show that under the variable change r = ds and s=x, the original equation transforms into r+1 dr 2r+1
Given the ordinary differential equation dy da = a) Show that it is invariant under the GTPL y²+(x2x2)y 2³ - x(x + y) - (x + €)y x = x + €, y = I b) Show that under the variable change r = ds and s=x, the original equation transforms into r+1 dr 2r+1
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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Prove it

Transcribed Image Text:Given the ordinary differential equation
dy
da
=
a) Show that it is invariant under the GTPL
y²+(x2x2)y 2³
-
x(x + y)
-
(x + €)y
x = x + €,
y =
I
b) Show that under the variable change r =
ds
and s=x, the original equation transforms into
r+1
dr
2r+1
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