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