Differential Equations

differential equations

In this post we define differential, ordinary equations and partial differential equations. Some examples of above topics are also provided.

A differential equation is an equation involving one dependent variable and its derivatives with respect to one or more independent variables.

Examples:

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

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