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

Example of Differential Equation
Ordinary non-linear differential equation of the $2$nd order and $2$nd degree:
 * $\paren {1 + \paren {\dfrac {\d y} {\d x} }^2}^{3/2} = 3 \dfrac {\d^2 y} {\d x^2}$

Proof
Squaring both sides gives:


 * $\paren {1 + \paren {\dfrac {\d y} {\d x} }^2}^3 = 9 \paren {\dfrac {\d^2 y} {\d x^2} }^2$

It is seen that the term in $\dfrac {\d^2 y} {\d x^2}$ is squared.

Hence the result by definition of degree.