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Putnam
1953 Putnam
B3
Putnam 1953 B3
Putnam 1953 B3
Source: Putnam 1953
July 16, 2022
Putnam
differential equation
Problem Statement
Solve the equations
d
y
d
x
=
z
(
y
+
z
)
n
,
d
z
d
x
=
y
(
y
+
z
)
n
,
\frac{dy}{dx}=z(y+z)^n, \;\; \; \frac{dz}{dx} = y(y+z)^n,
d
x
d
y
=
z
(
y
+
z
)
n
,
d
x
d
z
=
y
(
y
+
z
)
n
,
given the initial conditions
y
=
1
y=1
y
=
1
and
z
=
0
z=0
z
=
0
when
x
=
0.
x=0.
x
=
0.
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