Differential Equation/Examples/Second Order Non-Linear Ordinary
Jump to navigation
Jump to search
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: $(3.16)$