# Differential Equations

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

1. ### Partial Differential Equations

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

Examples:

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