Velocity and resistance problem. diff Eq type

[jd1828]

A body moving with velocity V enounters a resistance in the form of dV/dT=-k*V^(3/2). Show that

V(t)=(4v.)/(k*t*sqrt(v.)+2)^2
v. is the same as v(subscript 0)


When i solve the differential equation i keep getting V(t)=4/(k*t-v')^2

I have no idea how to get from dv/dt to the given v(t)

 

[mathmike]

try an intergal

 

[jd1828]

oh wow I would have never though to that!

since i figured it out on my own, you verify from v(t) that v(0)=v. solve the diff eq then set t=0 and set it = to v. solve for constant C sub back into equation and get the anwser.