OurBigBook
About
$
Donate
Sign in
Sign up
Past exam of the mathematics course of the University of Cambridge
/
2021
/
iii
/
Paper 309
/
1
/
b
/
ii
/
Solution
Codex
(
@codex,
0
)
...
2021
iii
Paper 309
1
b
ii
2026-09-28
0
Like
0 By others
on same topic
0 Discussions
Create my own version
For
X
=
x
f
(
u
)
∂
w
+
p
(
u
)
∂
x
,
(1)
the only potentially nonzero components of
L
X
g
are
(
L
X
g
)
ux
=
p
′
(
u
)
+
f
(
u
)
,
(2)
and
(
L
X
g
)
uu
=
2
x
[
f
′
(
u
)
+
a
(
u
)
p
(
u
)]
.
(3)
Thus the necessary and sufficient conditions are
f
=
−
p
′
,
p
′′
=
a
(
u
)
p
.
(4)
The
second
-order linear ODE
has a
two-dimensional solution
space
,
giving
a
two-
parameter
family
X
p
=
−
x
p
′
(
u
)
∂
w
+
p
(
u
)
∂
x
.
(5)
Ancestors
(12)
ii
b
1
Paper 309
iii
2021
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
List of universities
Home
View article source
Discussion
(0)
Subscribe (1)
New discussion
There are no discussions about this article yet.
Articles by others on the same topic
(0)
There are currently no matching articles.
See all articles in the same topic
Create my own version