Answer
The function is not a solution of the differential equation.
Work Step by Step
Begin by solving for the fourth derivative of y.
$y=2sin(x)$
$y'= 2cos(x)$
$y''= -2sin(x)$
$y'''= -2cos(x)$
$y^{(4)}= 2sin(x)$
Then substitute back into the differential equation
$y^{(4)} - 16y=0$
$(2sin(x)) - 32sin(x)=0$
$-30sin(x) = 0$
Since both sides are not equal then the function is not a solution of the differential equation.
