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Mathematics
Problem
A function
y
=
y
(
x
)
y=y(x)
y
=
y
(
x
)
satisfies
d
y
d
x
=
x
+
2
(
x
−
1
)
x
+
4
\dfrac{dy}{dx}=\dfrac{x+2}{(x-1)\sqrt{x+4}}
d
x
d
y
=
(
x
−
1
)
x
+
4
x
+
2
and passes through
(
−
3
,
0
)
(-3,0)
(
−
3
,
0
)
. Taking into account all restrictions in the expression, what is the maximal open interval on which this particular solution is valid? a)
(
−
4
,
∞
)
(-4,\infty)
(
−
4
,
∞
)
b)
(
−
∞
,
1
)
(-\infty,1)
(
−
∞
,
1
)
c)
(
−
4
,
1
)
(-4,1)
(
−
4
,
1
)
d)
(
−
4
,
1
]
(-4,1]
(
−
4
,
1
]
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