Thank you for watching. For the stream function, the v-component of velocity is v = - partial psi / partial x. With the computed stream function this gives v=-2xy. Unlike computing velocity from the potential function, computing the v-component of velocity from the stream function introduces a minus sign.
The other reply is mistaken about where exactly that constant comes from. When solving an exact differential equation in the "total differential" form, (stuff) = df, you automatically also have df=0. So when you find f(x,y,z) from the first equation (the "total differential"), you also have f(x,y,z)=C by integrating the second equation (df=0). The point is, the streamline expression is equal to a constant because all solutions to exact differential equations resulting from integrating a total differential pop out as a function equal to a constant.
