# Ordinary differential equation

## Main Question or Discussion Point

what is the word ordinary mean? Why is it called so.

Am i correct to say that the solution of a differential equation is got by
integrating that equation.

## Answers and Replies

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chandran said:
what is the word ordinary mean? Why is it called so.
An ordinary differential equation has derivatives with respect to one variable.

$$\frac{dy(x)}{dx} + x = 0$$

Oridnary is there to separate it from partial differential equations, which have derivatives with respect to multiple variables.

$$\frac{\partial y(t,x,z)}{\partial t}+\frac{\partial^2 y(t,x,z)}{\partial x^2} = z$$

Last edited:
dextercioby
Science Advisor
Homework Helper
Ordinary means that the derivatives involved are taken wrt the only variable the unknown function depends on.

"Integrating",not literally on every occasion.But u can make an abuse of language and call solving an ODE/PDE "integrating" it.

Daniel.

Pyrrhus
Homework Helper
Ordinary to differential equations with total differentials.

Example of ODE

$$x^2 \frac{d^2 y}{dt^2} + x \frac{dy}{dt} + 15 = 0$$

There are a lot of methods to solve a differential equation...

dextercioby
Science Advisor
Homework Helper
Cyclovenom said:
Ordinary to differential equations with total differentials.

Example of ODE

$$x^2 \frac{d^2 y}{dt^2} + x \frac{dy}{dt} + 15 = 0$$

There are a lot of methods to solve a differential equation...
I would be very careful with total differentials,if i were you.

Daniel.