How Can I Use Calculus to Verify This Physics Equation?

[strawberryy]

I'm supposed to use calculus to verify that v(t) = sqrt(gm/c_d)tanh((sqrt(gc_d/m)t)

is a solution to dv/dt=g-(c_d/m)v². I don't understand what was done to achieve the solution.

 

[Hurkyl]

While the derivation isn't hard, you aren't being asked to solve the differential equation as if you had no guess at the form of the solution space -- you are simply being asked to verify that that is a solution.

 

[LawlQuals]

Agreed, what you list as a question is different than what you actually profess confusion in understanding.

The question wants you to verify v(t) is a solution. Did you misunderstand, or did you really wish to discuss how to obtain that solution?