## Calculus 10th Edition

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.