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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \]

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

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \]

\[ {}9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0 \]

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y = 0 \]

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

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \]

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

\[ {}\left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y = 0 \]

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

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

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

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

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

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

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

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

\[ {}t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x = 0 \]

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

\[ {}x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z = 0 \]

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

\[ {}4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0 \]

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

\[ {}3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0 \]

\[ {}t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0 \]

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-\frac {1}{25}\right ) y = 0 \]

\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0 \]

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

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

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

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

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

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

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

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

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