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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (y+3 x -1\right )^{2} y^{\prime }-\left (2 y-1\right ) \left (4 y+6 x -3\right ) = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (10 x^{3} y^{2}+x^{2} y+2 x \right ) y^{\prime }+5 x^{2} y^{3}+x y^{2} = 0 \]

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

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

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

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

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

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

\[ {}\left (20 y^{3}-3 x y^{2}+6 x^{2} y+3 x^{3}\right ) y^{\prime }-y^{3}+6 x y^{2}+9 x^{2} y+4 x^{3} = 0 \]

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

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

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

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

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

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

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

\[ {}\left (7 x y^{3}+y-5 x \right ) y^{\prime }+y^{4}-5 y = 0 \]

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

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

\[ {}\left (10 x^{2} y^{3}-3 y^{2}-2\right ) y^{\prime }+5 y^{4} x +x = 0 \]

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

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

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

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

\[ {}\left (y^{4} x +2 x^{2} y^{3}+2 y+x \right ) y^{\prime }+y^{5}+y = 0 \]

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

\[ {}y^{m} x^{n} \left (a x y^{\prime }+b y\right )+\alpha x y^{\prime }+\beta y = 0 \]

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

\[ {}\frac {y^{\prime } f_{\nu }\left (x \right ) \left (-y+y^{p +1}\right )}{y-1}-\frac {g_{\nu }\left (x \right ) \left (-y+y^{q +1}\right )}{y-1} = 0 \]

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

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

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

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

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

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

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

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

\[ {}\left (\frac {\operatorname {e1} \left (x +a \right )}{\left (\left (x +a \right )^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {\operatorname {e2} \left (x -a \right )}{\left (\left (x -a \right )^{2}+y^{2}\right )^{\frac {3}{2}}}\right ) y^{\prime }-y \left (\frac {\operatorname {e1}}{\left (\left (x +a \right )^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {\operatorname {e2}}{\left (\left (x -a \right )^{2}+y^{2}\right )^{\frac {3}{2}}}\right ) = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}3 y^{\prime } \sin \left (x \right ) \sin \left (y\right )+5 \cos \left (x \right )^{4} y = 0 \]

\[ {}y^{\prime } \cos \left (a y\right )-b \left (1-c \cos \left (a y\right )\right ) \sqrt {\cos \left (a y\right )^{2}-1+c \cos \left (a y\right )} = 0 \]

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

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

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

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