\[ {}x y y^{\prime } = a \,x^{n}+b y^{2} \]

\[ x^{-2 b} \left (\frac {a \,x^{n}}{-n +2 b}+\frac {y^{2}}{2}\right ) = c_{1} \] Verified OK.

\[ {}x y y^{\prime } = \left (x^{2}+1\right ) \left (1-y^{2}\right ) \]

\[ -\frac {x^{2}}{2}-\ln \left (x \right )-\frac {\ln \left (y-1\right )}{2}-\frac {\ln \left (y+1\right )}{2} = c_{1} \] Verified OK.

\[ {}\left (2+3 x -x y\right ) y^{\prime }+y = 0 \]

\[ y^{3} {\mathrm e}^{-y} x -2 \left (y^{2}+2 y+2\right ) {\mathrm e}^{-y} = c_{1} \] Verified OK.

\[ {}x \left (4+y\right ) y^{\prime } = 2 x +2 y+y^{2} \]

\[ -\frac {\ln \left (-x +y\right )}{2}+\frac {\ln \left (-x +2 y+4\right )}{4} = -\frac {\ln \left (x \right )}{4}+c_{1} \] Verified OK.

\[ {}x \left (x +y\right ) y^{\prime }+y^{2} = 0 \]

\[ \ln \left (y\right )-\frac {\ln \left (2 y+x \right )}{2} = -\frac {\ln \left (x \right )}{2}+c_{1} \] Verified OK.

\[ {}x \left (x -y\right ) y^{\prime }+2 x^{2}+3 x y-y^{2} = 0 \]

\[ \frac {x^{4}}{2}+y x^{3}-\frac {x^{2} y^{2}}{2} = c_{1} \] Verified OK.

\[ {}x \left (4 x -y\right ) y^{\prime }+4 x^{2}-6 x y-y^{2} = 0 \]

\[ \ln \left (2 x +y\right )-\frac {\ln \left (-x +y\right )}{2} = -\frac {\ln \left (x \right )}{2}+c_{1} \] Verified OK.

\[ {}x \left (x^{3}+y\right ) y^{\prime } = \left (x^{3}-y\right ) y \]

\[ \frac {\ln \left (y\right )}{2}-\frac {\ln \left (x^{3}+2 y\right )}{4} = -\frac {\ln \left (x \right )}{4}+c_{1} \] Verified OK.

\[ {}x \left (2 x^{3}+y\right ) y^{\prime } = \left (2 x^{3}-y\right ) y \]

\[ \frac {\ln \left (y\right )}{2}-\frac {\ln \left (x^{3}+y\right )}{4} = -\frac {\ln \left (x \right )}{4}+c_{1} \] Verified OK.

\[ {}x \left (2 x^{3}+y\right ) y^{\prime } = 6 y^{2} \]

\[ \frac {\ln \left (y\right )}{3}-\frac {2 \ln \left (-2 x^{3}+y\right )}{3} = -2 \ln \left (x \right )+c_{1} \] Verified OK.

\[ {}2 x y y^{\prime }+1-2 x^{3}-y^{2} = 0 \]

\[ \frac {-x^{3}+y^{2}-1}{x} = c_{1} \] Verified OK.

\[ {}2 x y y^{\prime }+a +y^{2} = 0 \]

\[ -\ln \left (x \right )-\ln \left (a +y^{2}\right ) = c_{1} \] Verified OK.

\[ {}2 x y y^{\prime } = x a +y^{2} \]

\[ -a \ln \left (x \right )+\frac {y^{2}}{x} = c_{1} \] Verified OK.

\[ {}x^{2}+y^{2}+2 x y y^{\prime } = 0 \]

\[ \frac {x^{3}}{3}+x y^{2} = c_{1} \] Verified OK.

\[ {}2 x y y^{\prime } = x^{2}+y^{2} \]

\[ -x +\frac {y^{2}}{x} = c_{1} \] Verified OK.

\[ {}2 x y y^{\prime } = 4 x^{2} \left (2 x +1\right )+y^{2} \]

\[ -4 x^{2}-4 x +\frac {y^{2}}{x} = c_{1} \] Verified OK.

\[ {}2 x y y^{\prime }+x^{2} \left (a \,x^{3}+1\right ) = 6 y^{2} \]

\[ \frac {y^{2}}{x^{6}}-\frac {1}{4 x^{4}}-\frac {a}{x} = c_{1} \] Verified OK.

\[ {}\left (3-x +2 x y\right ) y^{\prime }+3 x^{2}-y+y^{2} = 0 \]

\[ x \left (x^{2}+y^{2}-y\right )+3 y = c_{1} \] Verified OK.

\[ {}x \left (x -2 y\right ) y^{\prime }+y^{2} = 0 \]

\[ -\frac {y^{2}}{x}+y = c_{1} \] Verified OK.

\[ {}x \left (x -2 y\right ) y^{\prime }+\left (2 x -y\right ) y = 0 \]

\[ y x \left (x -y\right ) = c_{1} \] Verified OK.

\[ {}x \left (1+x -2 y\right ) y^{\prime }+\left (1-2 x +y\right ) y = 0 \]

\[ -\frac {3 \left (1+y+x \right )}{\left (y x \right )^{\frac {1}{3}}} = c_{1} \] Verified OK.

\[ {}x \left (1-x -2 y\right ) y^{\prime }+\left (2 x +y+1\right ) y = 0 \]

\[ \frac {-3+3 x -3 y}{\left (y x \right )^{\frac {1}{3}}} = c_{1} \] Verified OK.

\[ {}2 x \left (2 x^{2}+y\right ) y^{\prime }+\left (12 x^{2}+y\right ) y = 0 \]

\[ 4 y x^{3}+x y^{2} = c_{1} \] Verified OK.

\[ {}2 \left (1+x \right ) y y^{\prime }+2 x -3 x^{2}+y^{2} = 0 \]

\[ x y^{2}-x^{3}+y^{2}+x^{2} = c_{1} \] Verified OK.

\[ {}x \left (2 x +3 y\right ) y^{\prime } = y^{2} \]

\[ \ln \left (y\right )+\frac {\ln \left (x +y\right )}{2} = \frac {\ln \left (x \right )}{2}+c_{1} \] Verified OK.

\[ {}x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2} = 0 \]

\[ \frac {3 x^{4}}{4}+2 y x^{3}+\frac {3 x^{2} y^{2}}{2} = c_{1} \] Verified OK.

\[ {}\left (3+6 x y+x^{2}\right ) y^{\prime }+2 x +2 x y+3 y^{2} = 0 \]

\[ x \left (y x +3 y^{2}+x \right )+3 y = c_{1} \] Verified OK.

\[ {}3 x \left (2 y+x \right ) y^{\prime }+x^{3}+3 y \left (y+2 x \right ) = 0 \]

\[ \frac {x^{4}}{4}+3 y x^{2}+3 x y^{2} = c_{1} \] Verified OK.

\[ {}a x y y^{\prime } = x^{2}+y^{2} \]

\[ \frac {a \,x^{-\frac {2}{a}} \left (a y^{2}-y^{2}-x^{2}\right )}{2 a -2} = c_{1} \] Verified OK.

\[ {}a x y y^{\prime }+x^{2}-y^{2} = 0 \]

\[ \frac {a \,x^{-\frac {2}{a}} \left (a y^{2}-y^{2}+x^{2}\right )}{2 a -2} = c_{1} \] Verified OK.

\[ {}x \left (x -a y\right ) y^{\prime } = y \left (-x a +y\right ) \]

\[ x \left (a -1\right ) \left (x -y\right ) y \left (y x \right )^{\frac {2-a}{a -1}} = c_{1} \] Verified OK.

\[ {}\left (1-x^{2} y\right ) y^{\prime }+1-x y^{2} = 0 \]

\[ -\frac {x^{2} y^{2}}{2}+x +y = c_{1} \] Verified OK.

\[ {}x \left (x y+2\right ) y^{\prime } = 3+2 x^{3}-2 y-x y^{2} \]

\[ -\frac {x \left (x^{3}-x y^{2}-4 y+6\right )}{2} = c_{1} \] Verified OK.

\[ {}x \left (2-x y\right ) y^{\prime }+2 y-x y^{2} \left (1+x y\right ) = 0 \]

\[ -\ln \left (x \right )+\frac {1}{x y}-\frac {1}{x^{2} y^{2}} = c_{1} \] Verified OK.

\[ {}\left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right ) = 0 \]

\[ -\frac {\ln \left (x^{2}+1\right )}{2}+\frac {\ln \left (y-1\right )}{2}+\frac {\ln \left (y+1\right )}{2} = c_{1} \] Verified OK.

\[ {}\left (-x^{2}+1\right ) y y^{\prime }+2 x^{2}+x y^{2} = 0 \]

\[ \frac {\ln \left (x -1\right )}{2}+\frac {-y^{2}-2}{4 x -4}-\frac {\ln \left (x +1\right )}{2}+\frac {y^{2}-2}{4 x +4} = c_{1} \] Verified OK.

\[ {}2 x^{2} y y^{\prime } = x^{2} \left (2 x +1\right )-y^{2} \]

\[ \left (-x^{2}+y^{2}\right ) {\mathrm e}^{-\frac {1}{x}} = c_{1} \] Verified OK.

\[ {}x \left (1+2 x y\right ) y^{\prime }+\left (2+3 x y\right ) y = 0 \]

\[ y x^{2} \left (y x +1\right ) = c_{1} \] Verified OK.

\[ {}x \left (1+2 x y\right ) y^{\prime }+\left (1+2 x y-x^{2} y^{2}\right ) y = 0 \]

\[ -\ln \left (x \right )-\frac {2}{x y}-\frac {1}{2 x^{2} y^{2}} = c_{1} \] Verified OK.

\[ {}x^{2} \left (x -2 y\right ) y^{\prime } = 2 x^{3}-4 x y^{2}+y^{3} \]

\[ -\frac {\ln \left (-x +y\right )}{2}+\ln \left (-2 x +y\right )-\frac {\ln \left (x +y\right )}{2} = c_{1} -\ln \left (x \right ) \] Verified OK.

\[ {}2 \left (1+x \right ) x y y^{\prime } = 1+y^{2} \]

\[ -\ln \left (x \right )+\ln \left (x +1\right )+\ln \left (1+y^{2}\right ) = c_{1} \] Verified OK.

\[ {}3 x^{2} y y^{\prime }+1+2 x y^{2} = 0 \]

\[ \frac {3 x^{\frac {1}{3}} \left (x y^{2}+2\right )}{2} = c_{1} \] Verified OK.

\[ {}x^{2} \left (4 x -3 y\right ) y^{\prime } = \left (6 x^{2}-3 x y+2 y^{2}\right ) y \]

\[ \ln \left (x \right )-2 \ln \left (y\right )+\ln \left (x^{2}+y^{2}\right )+\frac {3 \arctan \left (\frac {y}{x}\right )}{2}-c_{1} = 0 \] Verified OK.

\[ {}\left (1-x^{3} y\right ) y^{\prime } = x^{2} y^{2} \]

\[ -\frac {y^{3} x^{3}}{3}+\frac {y^{2}}{2} = c_{1} \] Verified OK.

\[ {}2 x^{3} y y^{\prime }+a +3 x^{2} y^{2} = 0 \]

\[ x \left (x^{2} y^{2}+a \right ) = c_{1} \] Verified OK.

\[ {}x \left (3-2 x^{2} y\right ) y^{\prime } = 4 x -3 y+3 x^{2} y^{2} \]

\[ -x \left (x^{2} y^{2}+2 x -3 y\right ) = c_{1} \] Verified OK.

\[ {}8 x^{3} y y^{\prime }+3 x^{4}-6 x^{2} y^{2}-y^{4} = 0 \]

\[ \ln \left (x^{2}+y^{2}\right )-\ln \left (y^{2}-3 x^{2}\right ) = c_{1} -\ln \left (x \right ) \] Verified OK.

\[ {}x y \left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2} \]

\[ \frac {-\ln \left (x \right )+\frac {\ln \left (b \,x^{2}+a \right )}{2}}{a}+\frac {\ln \left (A +B y^{2}\right )}{2 B} = c_{1} \] Verified OK.

\[ {}3 x^{4} y y^{\prime } = 1-2 x^{3} y^{2} \]

\[ \frac {\frac {3 y^{2} x^{3}}{2}+\frac {3}{5}}{x^{\frac {5}{3}}} = c_{1} \] Verified OK.

\[ {}y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}} = 0 \]

\[ -\sqrt {1+y^{2}}-\sqrt {x^{2}+1} = c_{1} \] Verified OK.

\[ {}\left (y+1\right ) y^{\prime } \sqrt {x^{2}+1} = y^{3} \]

\[ -\operatorname {arcsinh}\left (x \right )-\frac {1}{y}-\frac {1}{2 y^{2}} = c_{1} \] Verified OK.

\[ {}y^{2} y^{\prime }+x \left (2-y\right ) = 0 \]

\[ 2 y+\frac {y^{2}}{2}+4 \ln \left (y-2\right )-\frac {x^{2}}{2} = c_{1} \] Verified OK.

\[ {}y^{2} y^{\prime } = x \left (1+y^{2}\right ) \]

\[ -\frac {x^{2}}{2}+y-\arctan \left (y\right ) = c_{1} \] Verified OK.

\[ {}\left (x +y^{2}\right ) y^{\prime }+y = b x +a \]

\[ -\left (\frac {b x}{2}+a -y\right ) x +\frac {y^{3}}{3} = c_{1} \] Verified OK.

\[ {}\left (x -y^{2}\right ) y^{\prime } = x^{2}-y \]

\[ -\frac {x^{3}}{3}+y x -\frac {y^{3}}{3} = c_{1} \] Verified OK.

\[ {}x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \]

\[ \frac {x^{2} y^{2}}{2}+\frac {y^{4}}{4} = c_{1} \] Verified OK.

\[ {}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y \]

\[ -\frac {x^{2}}{y}-y = c_{1} \] Verified OK.

\[ {}\left (x^{2}-y^{2}\right ) y^{\prime }+x \left (2 y+x \right ) = 0 \]

\[ \frac {x^{2} \left (x +3 y\right )}{3}-\frac {y^{3}}{3} = c_{1} \] Verified OK.

\[ {}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0 \]

\[ \frac {x^{2} \left (4 x +3 y\right )}{3}+\frac {y^{3}}{3} = c_{1} \] Verified OK.

\[ {}\left (1-x^{2}+y^{2}\right ) y^{\prime } = 1+x^{2}-y^{2} \]

\[ \frac {y^{2}}{4}+\frac {y x}{2}+\frac {\ln \left (-x +y\right )}{2} = -\frac {x^{2}}{4}+c_{1} \] Verified OK.

\[ {}\left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+2 x y = 0 \]

\[ y x^{2}+y a^{2}+\frac {y^{3}}{3} = c_{1} \] Verified OK.

\[ {}\left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+b^{2}+x^{2}+2 x y = 0 \]

\[ b^{2} x +\frac {x^{3}}{3}+y x^{2}+y a^{2}+\frac {y^{3}}{3} = c_{1} \] Verified OK.

\[ {}\left (x^{2}+y^{2}+x \right ) y^{\prime } = y \]

\[ -\arctan \left (\frac {x}{y}\right )+y = c_{1} \] Verified OK.

\[ {}\left (3 x^{2}-y^{2}\right ) y^{\prime } = 2 x y \]

\[ -\frac {x^{2}}{y^{3}}+\frac {1}{y} = c_{1} \] Verified OK.

\[ {}\left (x^{4}+y^{2}\right ) y^{\prime } = 4 x^{3} y \]

\[ -\frac {x^{4}}{y}+y = c_{1} \] Verified OK.

\[ {}y \left (y+1\right ) y^{\prime } = \left (1+x \right ) x \]

\[ -\frac {x^{3}}{3}+\frac {y^{3}}{3}-\frac {x^{2}}{2}+\frac {y^{2}}{2} = c_{1} \] Verified OK.

\[ {}\left (x^{2}+2 y+y^{2}\right ) y^{\prime }+2 x = 0 \]

\[ {\mathrm e}^{y} x^{2}+{\mathrm e}^{y} y^{2} = c_{1} \] Verified OK.

\[ {}\left (x^{3}+2 y-y^{2}\right ) y^{\prime }+3 x^{2} y = 0 \]

\[ y x^{3}-\frac {y^{3}}{3}+y^{2} = c_{1} \] Verified OK.

\[ {}\left (1+y+x y+y^{2}\right ) y^{\prime }+1+y = 0 \]

\[ \frac {{\mathrm e}^{y} x}{y+1}+\frac {y \,{\mathrm e}^{y}}{y+1} = c_{1} \] Verified OK.

\[ {}\left (2 x^{2}+4 x y-y^{2}\right ) y^{\prime } = x^{2}-4 x y-2 y^{2} \]

\[ -\frac {x^{3}}{3}+2 y x^{2}+2 x y^{2}-\frac {y^{3}}{3} = c_{1} \] Verified OK.

\[ {}3 y^{2} y^{\prime } = 1+x +a y^{3} \]

\[ \frac {\left (a^{2} y^{3}+x a +a +1\right ) {\mathrm e}^{-x a}}{a^{2}} = c_{1} \] Verified OK.

\[ {}\left (x^{2}-3 y^{2}\right ) y^{\prime }+1+2 x y = 0 \]

\[ y x^{2}-y^{3}+x = c_{1} \] Verified OK.

\[ {}3 \left (x^{2}-y^{2}\right ) y^{\prime }+3 \,{\mathrm e}^{x}+6 x y \left (1+x \right )-2 y^{3} = 0 \]

\[ 3 x^{2} {\mathrm e}^{2 x} y-y^{3} {\mathrm e}^{2 x}+{\mathrm e}^{3 x} = c_{1} \] Verified OK.

\[ {}\left (3 x^{2}+2 x y+4 y^{2}\right ) y^{\prime }+2 x^{2}+6 x y+y^{2} = 0 \]

\[ \frac {2 x^{3}}{3}+3 y x^{2}+x y^{2}+\frac {4 y^{3}}{3} = c_{1} \] Verified OK.

\[ {}\left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }+x^{2}-3 x y^{2} = 0 \]

\[ -\frac {3 x^{2} y^{2}}{2}+\frac {x^{3}}{3}+2 y^{3}+y = c_{1} \] Verified OK.

\[ {}\left (x -6 y\right )^{2} y^{\prime }+a +2 x y-6 y^{2} = 0 \]

\[ x \left (y x -6 y^{2}+a \right )+12 y^{3} = c_{1} \] Verified OK.

\[ {}\left (x^{2} a +2 x y-a y^{2}\right ) y^{\prime }+x^{2}-2 a x y-y^{2} = 0 \]

\[ \ln \left (x^{2}+y^{2}\right )-\ln \left (a y-x \right ) = c_{1} \] Verified OK.

\[ {}\left (x^{2} a +2 b x y+c y^{2}\right ) y^{\prime }+k \,x^{2}+2 a x y+b y^{2} = 0 \]

\[ y a \,x^{2}+b x y^{2}+\frac {k \,x^{3}}{3}+\frac {y^{3} c}{3} = c_{1} \] Verified OK.

\[ {}x \left (x^{2}+y^{2}\right ) y^{\prime } = \left (x^{2}+x^{4}+y^{2}\right ) y \]

\[ \frac {y^{2}}{2 x^{2}}+\ln \left (\frac {y}{x}\right )-\frac {x^{2}}{2}-c_{2} = 0 \] Verified OK.

\[ {}x \left (1-x^{2}+y^{2}\right ) y^{\prime }+\left (1+x^{2}-y^{2}\right ) y = 0 \]

\[ \frac {x^{2}+y^{2}-1}{x y} = c_{1} \] Verified OK.

\[ {}x \left (a -x^{2}-y^{2}\right ) y^{\prime }+\left (a +x^{2}+y^{2}\right ) y = 0 \]

\[ \frac {x^{2}-y^{2}-a}{x y} = c_{1} \] Verified OK.

\[ {}x \left (a +y\right )^{2} y^{\prime } = b y^{2} \]

\[ -\ln \left (x \right )+\frac {y-\frac {a^{2}}{y}+2 a \ln \left (y\right )}{b} = c_{1} \] Verified OK.

\[ {}x \left (x^{2}-x y-y^{2}\right ) y^{\prime } = \left (x^{2}+x y-y^{2}\right ) y \]

\[ -\frac {x}{y}-\ln \left (x \right )-\frac {y}{x}-\ln \left (y\right ) = c_{1} \] Verified OK.

\[ {}x \left (x^{2}+a x y+y^{2}\right ) y^{\prime } = \left (x^{2}+b x y+y^{2}\right ) y \]

\[ -\frac {x}{y}-\ln \left (x \right ) b +\frac {y}{x}+a \ln \left (y\right ) = c_{1} \] Verified OK.

\[ {}x \left (x^{2}-2 y^{2}\right ) y^{\prime } = \left (2 x^{2}-y^{2}\right ) y \]

\[ -\frac {3 \left (x^{2}+y^{2}\right )}{2 \left (y x \right )^{\frac {2}{3}}} = c_{1} \] Verified OK.

\[ {}x \left (x^{2}+2 y^{2}\right ) y^{\prime } = \left (2 x^{2}+3 y^{2}\right ) y \]

\[ -\ln \left (y\right )-\frac {\ln \left (x^{2}+y^{2}\right )}{2} = -3 \ln \left (x \right )+c_{1} \] Verified OK.

\[ {}3 x y^{2} y^{\prime } = 2 x -y^{3} \]

\[ x y^{3}-x^{2} = c_{1} \] Verified OK.

\[ {}\left (1-4 x +3 x y^{2}\right ) y^{\prime } = \left (2-y^{2}\right ) y \]

\[ \sqrt {y^{2}-2}\, y^{2} x +\sqrt {y^{2}-2} = c_{1} \] Verified OK.

\[ {}x \left (x -3 y^{2}\right ) y^{\prime }+\left (2 x -y^{2}\right ) y = 0 \]

\[ y x \left (x -y^{2}\right ) = c_{1} \] Verified OK.

\[ {}3 x \left (x +y^{2}\right ) y^{\prime }+x^{3}-3 x y-2 y^{3} = 0 \]

\[ \frac {x^{3}+y^{3}+3 y x}{x^{2}} = c_{1} \] Verified OK.

\[ {}6 x y^{2} y^{\prime }+x +2 y^{3} = 0 \]

\[ 2 x y^{3}+\frac {x^{2}}{2} = c_{1} \] Verified OK.

\[ {}x \left (x^{2}-6 y^{2}\right ) y^{\prime } = 4 \left (x^{2}+3 y^{2}\right ) y \]

\[ -\frac {\left (3 y^{2}+x^{2}\right )^{2}}{y}+9 y^{3} = c_{1} \] Verified OK.

\[ {}x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y = 0 \]

\[ 2 x \left (x -y^{2}\right ) y \sqrt {y x} = c_{1} \] Verified OK.

\[ {}x^{2} y^{2} y^{\prime }+1-x +x^{3} = 0 \]

\[ -\frac {x^{2}}{2}+\ln \left (x \right )+\frac {1}{x}-\frac {y^{3}}{3} = c_{1} \] Verified OK.

\[ {}x \left (1+x y^{2}\right ) y^{\prime }+y = 0 \]

\[ -\frac {1}{x y}+y = c_{1} \] Verified OK.

\[ {}x \left (1+x y^{2}\right ) y^{\prime } = \left (2-3 x y^{2}\right ) y \]

\[ \frac {x^{2} \left (x y^{2}-1\right )}{y} = c_{1} \] Verified OK.

\[ {}x^{2} \left (a +y\right )^{2} y^{\prime } = \left (x^{2}+1\right ) \left (y^{2}+a^{2}\right ) \]

\[ -x +\frac {1}{x}+y+\ln \left (y^{2}+a^{2}\right ) a = c_{1} \] Verified OK.

\[ {}\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right ) = 0 \]

\[ -\frac {\ln \left (x^{2}+1\right )}{2}+\frac {\ln \left (y-1\right )}{2}+\frac {\ln \left (y+1\right )}{2}-\frac {\ln \left (y\right )}{2} = c_{1} \] Verified OK.

\[ {}\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y\right )^{2} = 0 \]

\[ -\frac {\ln \left (x^{2}+1\right )}{2}-\frac {\ln \left (y\right )}{2}+\frac {1}{y-1} = c_{1} \] Verified OK.

\[ {}\left (1-x^{3}+6 x^{2} y^{2}\right ) y^{\prime } = \left (6+3 x y-4 y^{3}\right ) x \]

\[ 2 y^{3} x^{2}-y x^{3}-3 x^{2}+y = c_{1} \] Verified OK.