Answer
The function is a solution to the differential equation.
Work Step by Step
Begin by solving for the 4th derivative of y.
$y=3sin(2x)$
$y'=6cos(2x)$
$y''=-12sin(2x)$
$y'''= -24cos(2x)$
$y^{(4)} = 48sin(2x)$
Now substitute back into the differential equation
$48sin(2x) - 48sin(2x)=0$
$0=0$
Since both sides are equal, the function is a solution of the differential equation.
