Differential Equations

For the differential equation $\frac{d^2y}{dx^2} - 4\frac{dy}{dx} + 4y = 0$, the characteristic roots are $m_1 = m_2 = 2$. If $y(0) = 1$ and $y'(0) = 4$, then $y(x) = (1 + C_2 x) e^{2x}$. Since $y'(0) = C_2 + 2(1) = 4 \implies C_2 = 2$. The value of $y(1)$ divided by $e^2$ is: