Formation of Ordinary Differential Equation by Elimination/Examples/y equals A cos 3x + B sin 3x

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


 * $(1): \quad y = A \cos 3 x + B \sin 3 x$

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


 * $\dfrac {\d^2 y} {\d x^2} + 9 y = 0$

Proof
Differentiating twice $x$: