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

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

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

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

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

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

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

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

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

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

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

\[ {}{x^{\prime }}^{2}+t x = \sqrt {t +1} \]

\[ {}\cos \left (\theta \right ) v^{\prime }+v = 3 \]

\[ {}x^{\prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+7 y = 1 \]

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

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

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

\[ {}t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y = \ln \left (t \right ) \]

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {1}{\sqrt {15-x^{2}-y^{2}}} \]

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

\[ {}\left [y_{1}^{\prime }\left (x \right ) = \sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right ), y_{2}^{\prime }\left (x \right ) = \tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1\right ] \]

\[ {}\left [y_{1}^{\prime }\left (x \right ) = \sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right ), y_{2}^{\prime }\left (x \right ) = \tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1\right ] \]

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

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

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

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

\[ {}y^{\prime } = \left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right ) \]

\[ {}y^{\prime } = \left (y-1\right ) \left (y-2\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right ) \]

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

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

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

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

\[ {}y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime } = y \]

\[ {}x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y = 0 \]

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

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

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )-5] \]

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

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

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

\[ {}y^{\prime \prime }+4 y = t \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{\frac {3}{2}} \]

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

\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \]

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

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

\[ {}y^{\prime }-\tan \left (y\right ) = \frac {{\mathrm e}^{x}}{\cos \left (y\right )} \]

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

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

\[ {}4 x y^{\prime \prime }+2 y^{\prime }+y = 1 \]

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

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

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

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

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