# Is there a difference between an one-dimension differential equation and an ordinary differential equation (ODE)?

Is there a difference between an one-dimension differential equation and an ordinary differential equation (ODE)? Or do they mean the same thing?

Also, would anything like $\dot x = x^2+5x-4$ be considered an ODE or one-dimensional differential equation?

• ODE means that there is a single scalar independent variable, traditionally denoted by $t$. Generally the dimension of an ODE refers to the dimension of the space where the dependent variable lives. Thus your example is a "one-dimensional ODE". – Ian Sep 16 '16 at 23:11

I think that differential equations need to be at least two-dimensions. In your example, we are solving for the function $x$. Also, a two-dimensional differential equation is an ODE.