Is a differential equation ordinary if it only contains derivatives with respect to one variable, even if the function has multiple variables?
For example the function y=f(x,t) and the differential equation $\frac{d^2y}{dx^2}+2\frac{dy}{dx}=4$ would that be ordinary are partial?
Does the question not make sense because if you already know how many (independent) variables the function (in this case $y$) depends on, then it wouldn't be a differential equation because the function isn't unknown?
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$\begingroup$An ordinary differential equation is an equation which involves derivatives of one or more dependent variables with respect to a single independent variable.
Ex: $\frac{d^2y}{dx^2}+\frac{dy}{dx}+2=0$
A partial differential equation is an equation which involves partial derivatives of one or more dependent variables with respect to more than one independent variables.
Ex : $u_{xx}+u_{yy}=0$
In mathematics, an ordinary differential equation or ODE is an equation containing a function of one independent variable and its derivatives. The term "ordinary" is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.
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