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
A differential equation is an equation with at least one derivative in it.
A derivative deals with rates of change. So, a differential equation says that a rate of change is equal to something.
In early math courses, solutions are often a single number. Later on, solutions can be functions or equations.
For differential equations, we often want to solve for what function has the derivative that has the properties described by that differential equation.
For example, you may observe in nature that something is happening at a certain speed. You can write that down as a differential equation, because speed is the derivative of position (speed is how fast the position changes). Solving this differential equation means finding the equation that describes the position.
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