Which of the following functions (there may be more than one) are solutions of the differential equation
d
2
y
d
x
2
−
y
=
0
\displaystyle {\frac{{{d}^{{2}}{y}}}{{{\left.{d}{x}\right.}^{{2}}}}}-{y}={0}
d
x
2
d
2
y
−
y
=
0
?
y
=
−
cos
(
x
)
\displaystyle {y}=-{\cos{{\left({x}\right)}}}
y
=
−
cos
(
x
)
y
=
4
e
−
x
\displaystyle {y}={4}{e}^{{-{x}}}
y
=
4
e
−
x
y
=
0
\displaystyle {y}={0}
y
=
0
y
=
sin
(
x
)
\displaystyle {y}={\sin{{\left({x}\right)}}}
y
=
sin
(
x
)
y
=
e
x
\displaystyle {y}={e}^{{x}}
y
=
e
x
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