## Calculus 10th Edition

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.