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Mathematics
Mathematics
Problem
A curve in the plane satisfies
d
x
d
t
=
t
2
−
1
\dfrac{dx}{dt}=t^{2}-1
d
t
d
x
=
t
2
−
1
and
d
y
d
t
=
e
t
\dfrac{dy}{dt}=e^{t}
d
t
d
y
=
e
t
. The curve passes through
(
0
,
5
)
(0,5)
(
0
,
5
)
at
t
=
0
t=0
t
=
0
. Determine the equation for
y
(
t
)
y(t)
y
(
t
)
.
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