Solve the initial-value problem for
y
\displaystyle {y}
y
as a function of
x
\displaystyle {x}
x
.
(
81
−
x
2
)
d
y
d
x
=
1
\displaystyle {\left({81}-{x}^{{2}}\right)}\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}={1}
(
81
−
x
2
)
d
x
d
y
=
1
,
y
(
0
)
=
4
\displaystyle {y}{\left({0}\right)}={4}
y
(
0
)
=
4
y
=
\displaystyle {y}=
y
=
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