Multivariable DE and Momentum Problem

[jesusfreak324]

Ok, so I am doing a typical momentum problem with a varying mass (here dm/dt > 0). I am also taking into account air resistance (stoke's law essentially). After some manipulations I basically get:

6πnRv - mg(1 - p(water)/p(object)) = m (d/dt(v)) + v (d/dt(m))

I know I need to separate the variables but I am lost on how. Thank you for the assistance!

 

[HallsofIvy]

Ok, so I am doing a typical momentum problem with a varying mass (here dm/dt > 0). I am also taking into account air resistance (stoke's law essentially). After some manipulations I basically get:

6πnRv - mg(1 - p(water)/p(object)) = m (d/dt(v)) + v (d/dt(m))

I know I need to separate the variables but I am lost on how. Thank you for the assistance!

With only a single equation in two dependent variables, you can't. Just as you cannot solve a single equation for two unknowns.