The discussion revolves around the definition of a differential equation, particularly focusing on the terminology of "dependent variables" and "independent variables" as used in the context of differential equations. The scope includes conceptual clarification and technical explanation.
Participants generally agree on the definitions and roles of dependent and independent variables in differential equations, with no significant disagreement noted.
Some assumptions about the definitions of dependent and independent variables may not be explicitly stated, and the discussion does not delve into more complex scenarios involving multiple variables.
an equation containing the derivatives of one or more unknown functions(or dependent variables), with respect to one or more independent variables.
find_the_fun said:My textbook defines differential equation as
Could someone explain what is meant by the part in parenthesis "dependent variables"? I don't see the difference.
So in the case $$\frac{dy}{dx}$$ the$$ x$$ is referred to as the independent variable?mathmari said:When a differential equation involves one or more derivatives with respect to a particular variable, that variable is called the independent variable.
find_the_fun said:So in the case $$\frac{dy}{dx}$$ the$$ x$$ is referred to as the independent variable?