Question

Solve this differential equation? `(dv)/(dt)=g-((cr^2)/m)*v^2` given g,c,r,m are constants and v is f(t).

Answer 1

`v=sqrt[g/k] (tanh(sqrt[gk] (t+C_0)))`

Explanation:

This is a separable differential equation so

`(dv)/(g-k v ^2)=dt` with `k = ((cr^2)/m)`

Integrating

`("arctanh"(sqrt(k/g)v))/sqrt(k g) = t + C_0`

or

`v=sqrt[g/k] (tanh(sqrt[gk] (t+C_0)))`