Order of Differential Equation/Examples
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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:
- $x y^{\paren 4} + 2 y + \paren {x y'}^5 = x^3$