Order of Differential Equation/Examples

Examples of Orders of Differential Equations

First Order

The following ordinary differential equations are of the $1$st order:

$\dfrac {\d y} {\d x} + y = 0$

$y' = e^x$

$x y' = 2 y$

Second Order

The following ordinary differential equations are of the $2$nd order:

$\dfrac {\d^2 y} {\d x^2} = \dfrac 1 {1 - x^2}$

$\map {f'} x = \map {f''} x$

$y'' + \paren {3 y'}^3 + 2 x = 7$

Third Order

The following ordinary differential equation is of the $3$rd order:

$\paren {y'''}^2 + \paren {y''}^4 + y' = x$

Fourth Order

The following ordinary differential equation is of the $4$th order:

$x y^{\paren 4} + 2 y'' + \paren {x y'}^5 = x^3$