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

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## Example of Differential Equation

Ordinary non-linear differential equation of the $3$rd order and $2$nd degree:

- $\paren {\dfrac {\d^3 y} {\d x^3} }^2 + \paren {\dfrac {\d^2 y} {\d x^2} }^4 + \dfrac {\d y} {\d x} = x$

## Proof

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

The result follows 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: $(3.17)$