## Calculus 10th Edition

Begin by solving for the 4th derivative of y. $y= 5\ln{x}$ $y'= \frac{5}{x}$ $y''=- \frac{5}{x^2}$ $y'''= \frac{10}{x^3}$ $y^{(4)}= -\frac{30}{x^4}$ Substitute back into the differential eqution. $y^{(4)} -16y=0$ $-\frac{30}{x^4} -80\ln{x} \ne 0$ Since both sides are not equal, the function is not a solution of the differential equation.