Answer
$4Ce^{4x}=4Ce^{4x} \therefore y=Ce^{4x}$ is a solution of the differential equation $y'=4y$.
Work Step by Step
If we know the solution to a differential equation; we are able to verify the solution by taking its derivative and substituting it back into the differential equation
1. Given that $y=Ce^{4x}$
2. Compute the derivative $y'$
$y'=4\cdot Ce^{4x}=4Ce^{4x}$
3. Substitute into differential equation
$ \Rightarrow y'=4y \Rightarrow 4Ce^{4x}=4(Ce^{4x})$
4. Verification
$4Ce^{4x}=4Ce^{4x} \therefore y=Ce^{4x}$ is a solution of the differential equation $y'=4y$.
