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Mathematics
Problem
3. Prove that `
x
2
−
y
2
=
c
(
x
2
+
y
2
)
2
x^{2}-y^{2}=c\left(x^{2}+y^{2}\right)^{2}
x
2
−
y
2
=
c
(
x
2
+
y
2
)
2
` is the general solution of differential equation `
(
x
3
−
3
x
y
2
)
d
x
=
(
y
3
−
3
x
2
y
)
d
y
\left(x^{3}-3 x y^{2}\right) d x=\left(y^{3}-3 x^{2} y\right) d y
(
x
3
−
3
x
y
2
)
d
x
=
(
y
3
−
3
x
2
y
)
d
y
`, where `c` is a parameter.
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