Force Field 1

 

Problem 1.

A force field given by \[ \mathbf{F}(x,y)=\frac{2y}{\sqrt{x^2+y^2}}\mathbf{i}-\frac{y^2-x}{\sqrt{x^2+y^2}}\mathbf{j}. \] Draw it by finding and sketching the family of curves tangent to $\mathbf{F}$.