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Mathematics
Mathematics
Problem
The differential equation of the family of curves,
x
2
=
4
b
(
y
+
b
)
x^2 = 4b(y + b)
x
2
=
4
b
(
y
+
b
)
,
b
∈
R
b \in \mathbb{R}
b
∈
R
, is : (1)
x
(
y
′
)
2
=
x
+
2
y
y
′
x(y')^2 = x + 2yy'
x
(
y
′
)
2
=
x
+
2
y
y
′
(2)
x
(
y
′
)
2
=
2
y
y
′
−
x
x(y')^2 = 2yy' - x
x
(
y
′
)
2
=
2
y
y
′
−
x
(3)
x
y
′
′
=
y
′
xy'' = y'
x
y
′′
=
y
′
(4)
x
(
y
′
′
)
2
=
x
−
2
y
y
′
x(y'')^2 = x - 2yy'
x
(
y
′′
)
2
=
x
−
2
y
y
′
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