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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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