Chapter 14.1, Problem 54E

Flow curves in the plane Let $F\left(x,y\right)=\left(f\left(x,y\right),g\left(x,y\right)\right)$ be defined on ${ℝ}^2$.

54.    Find and graph the flow curves for the vector field F = 〈y, x〉. Note that $d/dx\left(y^2\right)=2y{y}^{\prime }\left(x\right)$