Formation of Ordinary Differential Equation by Elimination/Examples/y equals A e^2x + B e^-2x

Examples of Formation of Ordinary Differential Equation by Elimination
Consider the equation:


 * $(1): \quad y = A e^{2 x} + B e^{-2 x}$

This can be expressed as the ordinary differential equation of order $2$:


 * $\dfrac {\d^2 y} {\d x^2} = 4 y$

Proof
Differentiating twice $x$: