There are many different applications that they like to use with differential equations. I have done my best to provide you with a wide range of identifiers that you can use.

– The big one is that they use the term “differential equation” in the language of the problem. While you are technically working with differential equations at many different times previous to this, they usually only use the term differential equation when they want you to apply the techniques you have learned in the differential equation section.

–
Sometimes they will start you with a differential equation, usually looking something like $\frac{\mathit{dP}}{\mathit{dt}}$ or $\frac{\mathit{dB}}{\mathit{dt}}$ , usually *
with respect to time
*, $\frac{}{\mathit{dt}}$, and usually referred to as a *
rate
*at which something is happening. You will also notice that the differential equation at times includes the dependent variable (the *
y-piece
*) in its equation. This should jump out to you as usually see equations given in terms of the independent variable (the *
x-piece
*).

–
If you are given a differential equation like $\frac{d\textcolor[rgb]{}{B}}{d\textcolor[rgb]{}{t}}$, the equation is sometimes in terms of *
B
* instead of *
t
* as you might expect. Or you are given a $\frac{d\textcolor[rgb]{}{y}}{d\textcolor[rgb]{}{x}}$ in terms of *
y
*instead of in terms of *
x
*.

– You will be asked to find answers about what that rate, what that differential equation, is doing at a specific moment.

–
They can ask you to create a differential equation that *
models
* a given situation. When you are asked this, you will often times also be asked to find an initial value to go with the differential equation.

–
At times you will see the language of the problem include the words like *
proportional
* or *
inversely proportional
*.

These problems might seem similar to related rates problems from back in the derivative application section. What you will notice is different here is that you are not given multiple rates of change, differential equations, to work with, and are *
not
* being asked how some rate of change is occurring at a specific moment in time.

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