Fluid Mechanics: streamlines for a flow

[yrael]

Homework Statement

Show that the streamlines for a flow whose velocity components are u=c(x^2-y^2) and v=-2cxy, where c is a constant, are given by the equation x^2*y-y^3/3=constant. At which point (points) is the flow parallel to the y axis? At which point (points is the fluid stationary?

Homework Equations

dy/dx=v/u
u=c(x^2-y^2)
x^2*y-y^3/3=constant
v=-2cxy

The Attempt at a Solution

dy/dx=v/u=(-2cxy)/(c(x^2-y^2))=-2xy/(x^2-y^2)

intergral dy(x^2-y^2)=intergral -2xy dx
x^2y-1/3*y^3=-x^2y
ans y=sqrt(6)x?

How do i show what point is parallel to y-axis and what point is fluid stationary?

 

[Chestermiller]

It is parallel to the y-axis when dx/dy = 0, or, from the equations, when x = y. The fluid is stationary when u = v = 0.