What Does Ordinary Mean in Ordinary Differential Equations?

[chandran]

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.

 

[LeBrad]

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

 

[dextercioby]

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]

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]

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.