\[ {}12 x y+6 y^{3}+\left (9 x^{2}+10 x y^{2}\right ) y^{\prime } = 0 \]

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

\[ {}\frac {t y}{t^{2}+1}+y^{\prime } = 1-\frac {t^{3} y}{t^{4}+1} \]

\[ \int _{}^{t}-\frac {\textit {\_a}^{6}-2 \textit {\_a}^{5} y+\textit {\_a}^{4}-\textit {\_a}^{3} y+\textit {\_a}^{2}-\textit {\_a} y+1}{\sqrt {\textit {\_a}^{2}+1}\, \left (\textit {\_a}^{4}+1\right )^{\frac {3}{4}}}d \textit {\_a} = c_{1} \] Verified OK.

\[ {}\cos \left (y\right ) \sin \left (t \right ) y^{\prime } = \cos \left (t \right ) \sin \left (y\right ) \]

\[ -\ln \left (\sin \left (t \right )\right )+\ln \left (\sin \left (y\right )\right ) = c_{1} \] Verified OK.

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

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

\[ {}y^{\prime } = \frac {2 t}{y+t^{2} y} \]

\[ -\frac {\ln \left (t^{2}+1\right )}{2}+\frac {y^{2}}{4} = -\frac {\ln \left (5\right )}{2}+\frac {9}{4} \] Verified OK.

\[ {}\sqrt {t^{2}+1}\, y^{\prime } = \frac {t y^{3}}{\sqrt {t^{2}+1}} \]

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

\[ {}y^{\prime } = \frac {3 t^{2}+4 t +2}{-2+2 y} \]

\[ -t^{3}-2 t^{2}+y^{2}-2 t -2 y = 3 \] Verified OK.

\[ {}\cos \left (y\right ) y^{\prime } = -\frac {t \sin \left (y\right )}{t^{2}+1} \]

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

\[ {}y^{\prime } = k \left (a -y\right ) \left (b -y\right ) \]

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

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

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

\[ {}\left (t -\sqrt {t y}\right ) y^{\prime } = y \]

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

\[ {}y^{\prime } = \frac {t +y}{t -y} \]

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

\[ {}t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime } = 0 \]

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

\[ {}2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (t^{2} \cos \left (y\right )+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime } = 0 \]

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

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

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

\[ {}\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime } = 0 \]

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

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

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

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

\[ t^{3}+2 y t^{2}+y^{2} = 1 \] Verified OK.

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

\[ \frac {t^{2} y \left (y+2 t \right )}{2} = 10 \] Verified OK.

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

\[ t = \int _{}^{y}\frac {1}{{\mathrm e}^{\left (-t +\textit {\_a} \right )^{2}}-1}d \textit {\_a} +c_{1} \] Verified OK.

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {x}{y} \]

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

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

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

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

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

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

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

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

\[ \ln \left (\cos \left (x \right )\right )+\ln \left (\cos \left (y\right )\right ) = 0 \] Verified OK.

\[ {}y^{\prime } = {\mathrm e}^{y} \]

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

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

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

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

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

\[ {}y^{\prime } = \frac {2 x -y}{x +4 y} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}3 x -y+1+\left (x -3 y-5\right ) y^{\prime } = 0 \]

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

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

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

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

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

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

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

\[ {}x \left (6 x y+5\right )+\left (2 x^{3}+3 y\right ) y^{\prime } = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ -\frac {5 \ln \left (3 x^{2}+4 y^{2}\right )}{24}+\frac {2 \ln \left (y\right )}{3}+\frac {3 \ln \left (x \right )}{4} = c_{1} \] Verified OK.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}2 x^{2} y y^{\prime }+x^{4} {\mathrm e}^{x}-2 x y^{2} = 0 \]

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

\[ {}y \left (1-x^{4} y^{2}\right )+x y^{\prime } = 0 \]

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

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

\[ \frac {y \left (x^{2} y+1\right )}{x} = 7 \] Verified OK.

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

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

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

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

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

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

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

\[ \frac {2 x}{\sqrt {y}}-\frac {2 y^{\frac {7}{2}}}{7} = c_{1} \] Verified OK.

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

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

\[ {}y+y^{3}+4 \left (x y^{2}-1\right ) y^{\prime } = 0 \]

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

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

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

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

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

\[ {}y^{3} y^{\prime }+y^{4} x = x \,{\mathrm e}^{-x^{2}} \]

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

\[ {}\sin \left (\theta \right ) \theta ^{\prime }+\cos \left (\theta \right )-t \,{\mathrm e}^{-t} = 0 \]

\[ \frac {\left (1+2 t \right ) {\mathrm e}^{-2 t}}{4}-{\mathrm e}^{-t} \cos \left (\theta \right ) = c_{1} \] Verified OK.

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

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

\[ {}y^{\prime }-x y = \sqrt {y}\, x \,{\mathrm e}^{x^{2}} \]

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

\[ {}t x^{\prime }+x \left (1-x^{2} t^{4}\right ) = 0 \]

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

\[ {}y^{\prime }-x y = \frac {x}{y} \]

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

\[ {}r^{\prime }+\left (r-\frac {1}{r}\right ) \theta = 0 \]

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

\[ {}2 y+x y^{\prime } = 3 x^{3} y^{\frac {4}{3}} \]

\[ \frac {1}{y^{\frac {1}{3}}} = -\frac {3 x^{3}}{7}+c_{1} x^{\frac {2}{3}} \] Verified OK.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ \frac {2 y^{3}+6 x^{2}}{3 x^{\frac {3}{2}}} = c_{1} \] Verified OK.

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

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

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

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

\[ {}\sec \left (y\right )^{2} y^{\prime } = \tan \left (y\right )+2 x \,{\mathrm e}^{x} \]

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