Applications of First Order Ordinary Differential Equations

Differential equations model real-world change: their solutions predict how a system will behave at a future time or in an unknown location. In many practical problems the rate at which a quantity changes is a given function of the quantity itself and/or of time $t$ — if $x$ denotes the amount of the quantity present at time $t$, the instantaneous rate of change is $\dfrac{dx}{dt}$, leading to a differential equation of the form

$\dfrac{dx}{dt}=f(x,t).$ …