\[ {}y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y = 0 \]

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

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

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

\[ {}y^{\prime \prime }+2 k \,{\mathrm e}^{x \mu } y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+k^{2} {\mathrm e}^{2 x \mu }+k \mu \,{\mathrm e}^{x \mu }+c \right ) y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a +b -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 x \mu }+d \,{\mathrm e}^{x \mu }+k \right ) y = 0 \]

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

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

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

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

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

\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y = 10 x +\frac {10}{x} \]

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

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

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (\ln \left (x \right )+1\right )^{2} \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y = \frac {1}{x^{2}} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = 0 \]

\[ {}2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 x^{2} {y^{\prime }}^{2}+36 x y y^{\prime }+6 y^{2} = 0 \]

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

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

\[ {}x^{2} y^{\prime \prime \prime }-5 x y^{\prime \prime }+\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y = 0 \]

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

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

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

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

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

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

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

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

\[ {}\left (x^{3}+1\right ) y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+18 x y^{\prime }+6 y = 0 \]

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

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

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

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

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

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

\[ {}4 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }+y^{\prime } = 0 \]

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

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

\[ {}x^{\prime }+t x^{\prime \prime } = 1 \]

\[ {}\frac {x^{\prime }+t x^{\prime \prime }}{t} = -2 \]

\[ {}x^{\prime \prime } = -\frac {x}{t^{2}} \]

\[ {}x^{\prime \prime } = \frac {4 x}{t^{2}} \]

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

\[ {}t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t} = 0 \]

\[ {}t^{2} x^{\prime \prime }-7 t x^{\prime }+16 x = 0 \]

\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }-8 x = 0 \]

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

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

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

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

\[ {}x^{\prime \prime }+\frac {x^{\prime }}{t} = a \]