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Some Examples of Ordinary Differential Equations with Missing
x
or
y
This Demonstration solves ordinary differential equations of the forms
and
by introducing a new variable
.
In the first case, the procedure is as follows:
,
,
,
.
In the second case:
,
,
,
. In both cases a solution is given in parametric form:
,
.
Contributed by:
Izidor Hafner
THINGS TO TRY
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Reference
[1] L. E. Eljsgoljc,
Differential Equations and Variational Calculus
(in Russian), Moscow: Nauka, 1969 pp. 69–71.
RELATED LINKS
First-Order Ordinary Differential Equation
(
Wolfram
MathWorld
)
Linear First-Order Differential Equation
(
Wolfram Demonstrations Project
)
Some Homogeneous Ordinary Differential Equations
(
Wolfram Demonstrations Project
)
D'Alembert's Differential Equation
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
Izidor Hafner
"
Some Examples of Ordinary Differential Equations with Missing
x
or
y
"
http://demonstrations.wolfram.com/SomeExamplesOfOrdinaryDifferentialEquationsWithMissingXOrY/
Wolfram Demonstrations Project
Published: May 7, 2014
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