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Abel equation
It is an
ODE
that is cubic in the unknown function:
u
1
=
f
3
(
x
)
u
3
+
f
2
(
x
)
u
2
+
f
1
(
x
)
u
+
f
0
(
x
)
where
f
3
(
x
)
≠
0
.
See
wikipedia
for more info.