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

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

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

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

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

\[ {}\left (3 x +1\right ) \left (y^{\prime }\right )^{2}-3 \left (y+2\right ) y^{\prime }+9 = 0 \]

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

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

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

\[ {}\left (\mathit {a2} x +\mathit {c2} \right ) \left (y^{\prime }\right )^{2}+\left (\mathit {a1} x +\mathit {b1} y+\mathit {c1} \right ) y^{\prime }+\mathit {a0} x +\mathit {b0} y+\mathit {c0} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\mathit {d0} \relax (x ) \left (y^{\prime }\right )^{2}+2 \mathit {b0} \relax (x ) y y^{\prime }+\mathit {c0} \relax (x ) y^{2}+2 \mathit {d0} \relax (x ) y^{\prime }+2 \mathit {e0} \relax (x ) y+\mathit {f0} \relax (x ) = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (\mathit {b2} y+\mathit {a2} x +\mathit {c2} \right ) \left (y^{\prime }\right )^{2}+\left (\mathit {a1} x +\mathit {b1} y+\mathit {c1} \right ) y^{\prime }+\mathit {a0} x +\mathit {b0} y+\mathit {c0} = 0 \]

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

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

\[ {}x y \left (y^{\prime }\right )^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-x y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (\mathit {b2} y+\mathit {a2} x +\mathit {c2} \right )^{2} \left (y^{\prime }\right )^{2}+\left (\mathit {a1} x +\mathit {b1} y+\mathit {c1} \right ) y^{\prime }+\mathit {b0} y+\mathit {a0} +\mathit {c0} = 0 \]

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

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

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

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

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

\[ {}9 y^{4} \left (x^{2}-1\right ) \left (y^{\prime }\right )^{2}-6 x y^{5} y^{\prime }-4 x^{2} = 0 \]

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

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

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

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

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

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

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

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

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

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

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