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Prolongations of the projective vector fields on the line
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Analysis
Differential equation
Ordinary differential equation
Lie point symmetry of an ordinary differential equation
Prolongation of a vector field
Schwarzian derivative
2026-10-03
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For
u
j
=
u
(
j
)
, the
n
th
prolongations
of the
translation
, dilation, and special projective generators
acting
on the independent variable are
pr
(
n
)
(
∂
x
)
pr
(
n
)
(
x
∂
x
)
pr
(
n
)
(
x
2
∂
x
)
=
∂
x
,
=
x
∂
x
−
j
=
1
∑
n
j
u
j
∂
u
j
,
=
x
2
∂
x
−
j
=
1
∑
n
(
2
j
x
u
j
+
j
(
j
−
1
)
u
j
−
1
)
∂
u
j
.
(1)
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(9)
Schwarzian derivative
Prolongation of a vector field
Lie point symmetry of an ordinary differential equation
Ordinary differential equation
Differential equation
Analysis
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2019
/
ii
/
Paper 3
/
32C
/
b
/
Solution
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