Differentiating results in us knowing how large y-output changes compared to qan amount of x-input in the function f(x)=y.
Integrating is, uh, just “the summation” of all y-outputs as a result of x-inputs.
Now, what does a DE tell me? And what does solving it do?
In: Mathematics
An ELI5 way of talking about it would be saying sometimes you know how fast a thing is ***changing*** but you really want to know the thing itself.
For example, position. Maybe you don’t know your actual position, but you do have something that measures your speed (change in position). You can solve the equation involving the change in position to determine your actual position, as long as you know at least one value of the position at a given time.
Another example might be heating up water or something. You don’t have a thermometer, but if you know the starting temperature (room temperature) and how much heat you’ve put in, you can still solve for the temperature.
Latest Answers