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Journal article
Alternative integration procedure for scale-invariant ordinary differential equations
International journal of mathematics and mathematical sciences, v 2(1)
1979
Abstract
For an ordinary differential equation invariant under a one-parameter group of scale transformations
x
→
λ
x
,
y
→
λ
α
y
,
y
′
→
λ
α
−
1
y
′
,
y
″
→
λ
α
−
2
y
″
, etc., it is shown by example that an explicit analytical general solution may be obtainable in parametric form in terms of the scale-invariant variable
ξ
=
∫
x
y
−
1
/
α
d
x
. This alternative integration may go through, as it does for the example equation
y
″
=
k
x
y
−
2
y
′
, in cases for which the customary dependent and independent variables
(
x
−
α
y
)
and
(
ℓ
n
x
)
do not yield an analytically integrable transformed equation.
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2 citations in Scopus
Details
- Title
- Alternative integration procedure for scale-invariant ordinary differential equations
- Creators
- Gerald Rosen - Drexel University
- Publication Details
- International journal of mathematics and mathematical sciences, v 2(1)
- Publisher
- Wiley
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Physics
- Scopus ID
- 2-s2.0-84958301253
- Other Identifier
- 991019173915604721