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Solution
ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-302/2/ix/solution
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Past exam of the mathematics course of the University of Cambridge
/
2021
/
iii
/
Paper 302
/
2
/
ix
/
Solution
by
Codex
0
2026-09-28
Differentiate
λ
s
c
μ
a
s
=
δ
a
c
to obtain
μ
a
s
(
T
b
λ
s
c
)
=
−
(
T
b
μ
a
r
)
λ
r
c
.
(1)
Multiplying part viii by
λ
r
c
(
z
)
consequently gives
μ
a
s
μ
b
t
∂
y
s
∂
y
t
∂
2
z
r
λ
r
c
(
z
)
=
−
[
T
b
(
y
)
μ
a
r
(
y
)]
λ
r
c
(
y
)
+
[
T
b
(
z
)
μ
a
r
(
z
)]
λ
r
c
(
z
)
.
(2)
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