This is now first-order linear, so solve using the Integrating Factor method.
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?
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.
Surely you know that velocity is the derivative of displacement, or the other way, displacement is the antiderivative of velocity...