The motion of a body falling in a viscous medium differential equation help (:

The motion of a body falling in a viscous medium may be described by the equation:

m(dv/dt) = -bv-mg

where m, g, b are positive constants. The initial conditions are v(0) = 0 and x(0) = 0.Determine the velocity v(t) and displacement x(t) for t < 0.

Anyone able to help please?

Re: The motion of a body falling in a viscous medium differential equation help (:

This is now first-order linear, so solve using the Integrating Factor method.

Re: The motion of a body falling in a viscous medium differential equation help (:

Ok so I can get to v(t)=(-gm/b)(1+e^(-bt/m)) (is this correct?)

However, I am unsure now as to solve for x(t).

Sorry I have not yet learnt how to use the proper math writing on here.

Re: The motion of a body falling in a viscous medium differential equation help (:

I get

Surely you know that velocity is the derivative of displacement, or the other way, displacement is the antiderivative of velocity...