Using F=kvx in order to describe x as a function of t

[acedeno]

Homework Statement

The force acting on a particle of mass m is given by
F=kvx
in which k is a positive constant. The particle passes through the origin with the speed v naught at time t=0. Find x as a function of (t)

Homework Equations

F=ma
a=(dx/dt)(dv/dx)

The Attempt at a Solution

F=kvx

ma=kvx

a=kvx/m

(dx/dt)(dv/dx)=kvx/m

v(dv/dx)=kvx/m

dv/dx=kx/m

dv=(kx/m)dx

integral of both sides left in terms of dv and right in terms of dx

V-Vnaught=kx^2/2m

I'm not sure where to go from here. Help would be very much appreciated!

 

[acedeno]

Nevermind I figured it out. For anyone who's curious.

V=(kx^2/2m)+Vnaught
dx/dt=(kx^2/2m)+Vnaught
dx/((kx^2/2m)+Vnaught)=dt
then integrate both sides.