# Chapter 6 - Differential Equations - 6.1 Exercises - Page 403: 20

The function is a solution of the differential equation

#### Work Step by Step

Start by finding the fourth derivative of y. $y=3e^{2x} - 4\sin2x$ $y^{'} = 6e^{2x} +8\cos2x$ $y^{''} = 12e^{2x} +16\sin2x$ $y^{(3)} = 24e^{2x} -32\cos2x$ $y^{(4)} = 48e^{2x} -64 \sin2x$ Substitute back into the differential equation $y^{(4)} - 16y =0$ $(48e^{2x} -64 \sin2x)-(48e^{2x} +64 \sin2x) = 0$ $0=0$, The function is a solution of the differential equation.

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