Independent and Dependent Variable Meaning? Given a differential equation, for example: 

$\displaystyle \frac{d^2x}{dt^2} + a \frac{dx}{dt} + kx = 0$

Is there a reason why we call $x$ the dependent variable and $t$ the independent variable? Here is the definition from my textbook: 

If an equation involves the derivative of one variable with respect to another, then the former is called a dependent variable and  the latter an independent variable

So according to this definition it makes sense why $x$ and $t$ are assigned in this way but is there an intuitive reasoning behind this terminology? 

The idea is that $x$ is a function of $t$ --- $x$ depends on $t$ --- $t$ can be chosen arbitrarily (independent of anything else), and then the value of $x$ follows. This is for functions generally, not just for differential equations. 
