Question

An object of mass m is moving to the right and has a speed of vanda position of x_0 at t=0. A drag force of F_d=cv^2 acts ontheobject.

(a) Find the velocity of the particle as a function oftime
(b) Find the position of the particle as a function of time


So I tried this:
F_d= cv^2=ma
so a=cv^2/m
dv/dt=cv^2/m
dv=(cv^2/m)dt
intergrated both sides with respect to time
to get
-1/v(t)=ct/m + C
to get C I get t=0
and got c=1/v_0

Solving for v(t) I got
v(t)=-m/ct +v_0
as my final answer for (a)
What is wrong with this answer?
[It's wrong]

I solved b a similar way and got v(t)=(-m/c)ln(-ct/m + 1/v_0) +x_0+ ln(1/v_0)(m/c)
thats wrong too though

Any help would be greatly appreciated!