Formation of Ordinary Differential Equation by Elimination/Examples/y equals Ax + A^3

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


 * $(1): \quad y = A x + A^3$

This can be expressed as the ordinary differential equation:


 * $y = x \dfrac {\d y} {\d x} + \paren {\dfrac {\d y} {\d x} }^3$

Proof
Differentiating $x$: