So I have a system of equations:

Variables:

V(x) - x velocity
V(y) - y velocity
C(x) - x constant
C(y) - y constant
t - time
g - gravity constant
dx, dy, dt, dV(x), dV(y), etc. - you can guess what these are

Problem:

dV(x) = C(x)*V(x)^(2)*dt
dV(y) = (C(y)*V(x)^(2)+g)*dt
dt = dy/V(y) = dx/V(x)

solve for V(x) and V(y) in terms of x and y

What I've done so far:

dV(x) = C(x)*(dx^2/dt^2)*dt
dV(x) = C(x)*V(x)*dx
Vx^(-1)*dV(x) = C(x)*dx
Integrate both sides (c is assumed to be 0 here) to get
ln(abs(V(x))) = x*C(x)
e^(x*C(x)) = abs(V(x))

good so far, right?

I sub in e^(x*C(x)) for V(x) in the next equation

dV(y) = (C(y)*e^(2*x*C(x))+g)*dt
dV(y) = (C(y)*e^(2*x*C(x))+g)*(dy/V(y))
V(y)*dV(y) = (C(y)*e^(2*x*C(x))+g)*dy

Now I'm stuck because I don't know how to integrate this equation

Help, please!

V(x) is squared... Did I not put that in?

abs(V(x))^2 is the same as V(x)^2

They're constants... I should have called them c and k, but the way I used is the way the problem is stated

But shouldn't there be something done to the X in the exponent?

I know that is wrong though because when I plug numbers back in, I don't get the right result