Question:

A particle is moving with a velocity v=K(y^i+x^j), where K is a constant. The general equation for its path is:

xy=constant

y2=x2+constant

y=x2+constant

y2=x+constant

dx/dt=ky, dy/dt=kx
Now, dy/dx = (dy/dt)/(dx/dt) = x/y
⇒ydy=xdx
Integrating both side
y2=x2+c