Order and Degree of differential equation

differential equations

In this post we define Order and Degree of differential equation and also related examples and method to find the order and degree.

The order of differential equation is the order of the highest derivative appearing in the equation.

The degree of the differential equation is the greatest exponent of the highest order derivative that appears in the equation.

$\frac{dy}{dx}+ycosx=sinx$
$\frac{dy}{dx}=7x+5$
$\frac{dy}{dx}=cosx$
$\frac{d^2y}{dx^2}+xy \left ( \frac{dy}{dx} \right )^2=0$
$\left [1+ \left (\frac{dy}{dx} \right )^2 \right ]^{3/2}=\frac{d^2y}{dx^2}$
$\frac{dy}{dx} +\left [1+ \left (\frac{dy}{dx} \right )^2 \right ]^{3/2}=0$
$\frac{d^2y}{dx^2}+\lambda y=0$
$y^2 \frac{\partial z}{\partial x}+y \frac{\partial z}{\partial y}=ax$
$x \frac{\partial z}{\partial x}+y \frac{\partial z}{\partial y}=nx$
$\frac{\partial^2 u}{\partial x^2}+ \frac{\partial^2u}{\partial y^2}+ \frac{\partial^2u}{\partial z^2}=0$