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

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

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

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

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

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

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

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

\[ {}2 y^{\prime \prime } y-\left (y^{\prime }\right )^{2}-8 y^{3} = 0 \]

\[ {}2 y^{\prime \prime } y-\left (y^{\prime }\right )^{2}-8 y^{3}-4 y^{2} = 0 \]

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

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

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

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

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

\[ {}2 y^{\prime \prime } y-\left (y^{\prime }\right )^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4} = 0 \]

\[ {}2 y^{\prime \prime } y-\left (y^{\prime }\right )^{2}+3 f \relax (x ) y y^{\prime }+2 \left (f \relax (x )^{2}+f^{\prime }\relax (x )\right ) y^{2}-8 y^{3} = 0 \]

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

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

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

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

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

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

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

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

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

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

\[ {}4 y^{\prime \prime } y-3 \left (y^{\prime }\right )^{2}-12 y^{3} = 0 \]

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

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

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

\[ {}12 y^{\prime \prime } y-15 \left (y^{\prime }\right )^{2}+8 y^{3} = 0 \]

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

\[ {}a y y^{\prime \prime }+b \left (y^{\prime }\right )^{2}+\mathit {c4} y^{4}+\mathit {c3} y^{3}+\mathit {c2} y^{2}+\mathit {c1} y+\mathit {c0} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}8 \left (-x^{3}+1\right ) y y^{\prime \prime }-4 \left (-x^{3}+1\right ) \left (y^{\prime }\right )^{2}-12 x^{2} y y^{\prime }+3 x y^{2} = 0 \]

\[ {}\mathit {f0} \relax (x ) y y^{\prime \prime }+\mathit {f1} \relax (x ) \left (y^{\prime }\right )^{2}+\mathit {f2} \relax (x ) y y^{\prime }+\mathit {f3} \relax (x ) y^{2} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}-2 y \left (1-y\right ) y^{\prime \prime }+\left (1-3 y\right ) \left (y^{\prime }\right )^{2}-4 y y^{\prime } \left (f \relax (x ) y+g \relax (x )\right )+\left (1-y\right )^{3} \left (\mathit {f0} \relax (x )^{2} y^{2}-\mathit {f1} \relax (x )^{2}\right )+4 y^{2} \left (1-y\right ) \left (f \relax (x )^{2}-g \relax (x )^{2}-g^{\prime }\relax (x )-f^{\prime }\relax (x )\right ) = 0 \]

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

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

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

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

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

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

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

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

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

\[ {}y^{3} y^{\prime \prime }-a = 0 \]

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

\[ {}2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1 = 0 \]

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

\[ {}2 \left (c -y\right ) \left (-y+b \right ) \left (-y+a \right ) y^{\prime \prime }+\left (\left (-y+a \right ) \left (-y+b \right )+\left (c -y\right ) \left (-y+a \right )+\left (-y+b \right ) \left (c -y\right )\right ) \left (y^{\prime }\right )^{2}-\mathit {a0} \left (c -y\right )^{2} \left (-y+b \right )^{2} \left (-y+a \right )^{2}-\mathit {a1} \left (-y+b \right )^{2} \left (c -y\right )^{2}-\mathit {a2} \left (c -y\right )^{2} \left (-y+a \right )^{2}-\mathit {a3} \left (-y+b \right )^{2} \left (-y+a \right )^{2} = 0 \]

\[ {}\left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) \left (y^{\prime }\right )^{2} = 0 \]

\[ {}\left (4 y^{3}-a y-b \right ) \left (y^{\prime \prime }+f y^{\prime }\right )-\left (6 y^{2}-\frac {a}{2}\right ) \left (y^{\prime }\right )^{2} = 0 \]

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

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

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

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

\[ {}\sqrt {y}\, y^{\prime \prime }-a = 0 \]

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

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

\[ {}\left (b +a \left (\sin ^{2}\relax (y)\right )\right ) y^{\prime \prime }+a \left (y^{\prime }\right )^{2} \cos \relax (y) \sin \relax (y)+A y \left (c +a \left (\sin ^{2}\relax (y)\right )\right ) = 0 \]

\[ {}h \relax (y) y^{\prime \prime }+a D\relax (h )\relax (y) \left (y^{\prime }\right )^{2}+j \relax (y) = 0 \]

\[ {}h \relax (y) y^{\prime \prime }-D\relax (h )\relax (y) \left (y^{\prime }\right )^{2}-h \relax (y)^{2} j \left (x , \frac {y^{\prime }}{h \relax (y)}\right ) = 0 \]

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

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

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

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

\[ {}\left (\mathit {f1} y^{\prime }+\mathit {f2} y\right ) y^{\prime \prime }+\mathit {f3} \left (y^{\prime }\right )^{2}+\mathit {f4} \relax (x ) y y^{\prime }+\mathit {f5} \relax (x ) y^{2} = 0 \]

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