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*From some height a object*

*with mass m*is thrown . Determinate the law that describes how the velocity of fall v changes, if on the object, besides gravity, acts the force air resistance, which is proportional to velocity v (the proportionality coefficient is k), ie must be found v= f(t)Then, by the second Newton's law, we have.

$$m\cdot\frac{dv}{dt}=mg-kv$$

AND THEN, HERE'S WHAT I DON'T UNDERSTAND. My textbook says:

Is easy to proof that every function:

$$v=Ce^{-\frac{k}{m}t}+\frac{mg}{k}$$

Satisfies the first equation.

Can somebody explain me in detail, why is that true? Thanks.