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

\[ {}9 \sqrt {x}\, y^{\frac {4}{3}}-12 x^{\frac {1}{5}} y^{\frac {3}{2}}+\left (8 x^{\frac {3}{2}} y^{\frac {1}{3}}-15 x^{\frac {6}{5}} \sqrt {y}\right ) y^{\prime } = 0 \]

\[ {}y^{\prime } = {| y|}+1 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}{y^{\prime }}^{3}+\operatorname {a0} {y^{\prime }}^{2}+\operatorname {a1} y^{\prime }+\operatorname {a2} +\operatorname {a3} y = 0 \]

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

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

\[ {}8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2} = 27 x +27 y \]

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

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

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

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

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

\[ {}y^{\prime \prime } = \frac {3 k y^{2}}{2} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0 \]

\[ {}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0 \]

\[ {}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0 \]

\[ {}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0 \]

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

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

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

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

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

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

\[ {}y^{\prime \prime } = -\frac {\left (\left (1-4 a \right ) x^{2}-1\right ) y^{\prime }}{x \left (x^{2}-1\right )}-\frac {\left (\left (-v^{2}+x^{2}\right ) \left (x^{2}-1\right )^{2}+4 a \left (1+a \right ) x^{4}-2 a \,x^{2} \left (x^{2}-1\right )\right ) y}{x^{2} \left (x^{2}-1\right )^{2}} \]

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

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

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

\[ {}x^{3} y^{\prime \prime \prime }+\left (x +3\right ) x^{2} y^{\prime \prime }+5 \left (x -6\right ) x y^{\prime }+\left (4 x +30\right ) y = 0 \]

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

\[ {}\left (x^{2}-1\right )^{2} y^{\prime \prime \prime \prime }+10 x \left (x^{2}-1\right ) y^{\prime \prime \prime }+\left (24 x^{2}-8-2 \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )\right ) \left (x^{2}-1\right )\right ) y^{\prime \prime }-6 x \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )-2\right ) y^{\prime }+\left (\left (\mu \left (\mu +1\right )-\nu \left (\nu +1\right )\right )^{2}-2 \mu \left (\mu +1\right )-2 \nu \left (\nu +1\right )\right ) y = 0 \]

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

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

\[ {}y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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