# Differential Equation/Examples/Second Order Non-Linear Ordinary

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## Example of Differential Equation

Ordinary non-linear differential equation of the $2$nd order:

- $\dfrac {\d^2 y} {\d x^2} + \paren {3 \dfrac {\d y} {\d x} }^3 + 2 x = 7$

## Proof

The term in $\dfrac {\d y} {\d x}$ is raised to the $3$rd degree and so the equation is non-linear.

The term in $\dfrac {\d^2 y} {\d x^2}$ is to the $1$st degree.

Hence the result by definition of degree.

$\blacksquare$

## Sources

- 1963: Morris Tenenbaum and Harry Pollard:
*Ordinary Differential Equations*... (previous) ... (next): Chapter $1$: Basic Concepts: Lesson $3$: The Differential Equation: $(3.16)$