Instead start by saying y=vx; therefore, dy=xdv+vdx.

Now take your de and multiple by dx to both sides and you will be left with dy = all that stuff.

Subtract all that stuff to obtain:

dy-(blah)dx=0

From taking the derivative of y=vx, we know dy=xdv+vdx. Substitute that in where you see dy and sub in vx where ever there are xs.