Chapter 9.1, Problem 20E

Verifying solutions of initial value problems Verify that the given function y is a solution of the initial value problem that follows it.

14.     $y\left(x\right)=\frac{1}{4}\left(e^{2x}-e^{-2x}\right);y^{″}\left(x\right)-4y\left(x\right)=0,y\left(0\right)=0,y^{\prime }\left(0\right)=1$