\[ {}u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5} = \cos \left (t \right ) \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}y y^{\prime \prime }+{y^{\prime }}^{2}+4 = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}3 y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}-1 \]

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

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

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

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

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

\[ {}3 y y^{\prime \prime }+y = 5 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+d +b x y+c y+a y^{3} = 0 \]

\[ {}y^{\prime \prime }+d +b y^{2}+c y+a y^{3} = 0 \]

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

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

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

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

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

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

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

\[ {}y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}+b \]

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

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

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

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

\[ {}x^{3} \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )+12 x y+24 = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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