Using PGFPlotstable, we can use a naive numerical integration scheme to find the function directly within LaTeX.
Edit and compile if you like:\documentclass[border=10pt]{standalone} \usepackage{pgfplots} \pgfplotsset{width=7cm,compat=1.8} \usepackage{pgfplotstable} \pgfplotstableset{ create on use/x/.style={ create col/expr={ \pgfplotstablerow/201*2-1 } }, create on use/y/.style={ create col/expr accum={ \pgfmathaccuma+(2/201)*(abs(\pgfmathaccuma^2)+abs(\thisrow{x}^2)-1) }{0.6} } } \pgfplotstablenew{201}\loadedtable \begin{document} \begin{tikzpicture} \begin{axis}[ view = {0}{90}, domain = -1:1, y domain = -1:1, samples = 21, xmax = 1, ymax = 1 ] \addplot3 [gray, quiver={u={1}, v={x^2+y^2-1}, scale arrows=0.075, every arrow/.append style={-latex}}] (x,y,0); \addplot [thick, red] table [x=x, y=y] {\loadedtable}; \end{axis} \end{tikzpicture} \end{document}