Answer to Question #231174 in Differential Equations for Randal Rodriguez

Question

verify that each given function is a solution of the

differential equation.

5.y′′\:−\:y\:=\:0;\:y\left(t\right)\:=\:e^t

Answer 1

Let us verify that the function $y(t)=e^t$ is a solution of the differential equation $y''-y=0$. Since $y'(t)=e^t$ and $y''(t)=e^t,$ we conclude that $y''(t)-y(t)=e^t-e^t=0,$ and hence $y(t)=e^t$ is a solution of the differential equation $y''-y=0$.