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Mathematics
Problem
For which ordered pair
(
a
,
b
)
(a,b)
(
a
,
b
)
does the function
y
(
x
)
=
(
x
2
+
a
x
+
b
)
e
x
y(x)=(x^{2}+a x+b)\,e^{x}
y
(
x
)
=
(
x
2
+
a
x
+
b
)
e
x
satisfy the differential equation
d
y
d
x
=
(
x
2
+
4
x
+
5
)
e
x
\dfrac{dy}{dx}=(x^{2}+4x+5)\,e^{x}
d
x
d
y
=
(
x
2
+
4
x
+
5
)
e
x
? a)
(
2
,
5
)
(2,5)
(
2
,
5
)
b)
(
4
,
5
)
(4,5)
(
4
,
5
)
c)
(
2
,
3
)
(2,3)
(
2
,
3
)
d)
(
3
,
2
)
(3,2)
(
3
,
2
)
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