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

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

\[ {}x^{3} y^{\prime \prime }+y = \frac {1}{x^{4}} \]

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

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

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

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

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

\[ {}x^{3} \left (x^{2}-25\right ) \left (-2+x \right )^{2} y^{\prime \prime }+3 x \left (-2+x \right ) y^{\prime }+7 \left (x +5\right ) y = 0 \]

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

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

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

\[ {}y^{\prime \prime \prime }-2 x y^{\prime \prime }+4 x^{2} y^{\prime }+8 x^{3} y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right . \]

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

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

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

\[ {}y^{\prime \prime }+5 x y^{\prime }+\sqrt {x}\, y = 0 \]

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

\[ {}x^{3} \left (x^{2}-25\right ) \left (-2+x \right )^{2} y^{\prime \prime }+3 x \left (-2+x \right ) y^{\prime }+7 \left (x +5\right ) y = 0 \]

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

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

\[ {}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right )+{\mathrm e}^{-t} \sin \left (2 t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+9 z \left (t \right )+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ), z^{\prime }\left (t \right ) = y \left (t \right )+6 z \left (t \right )-{\mathrm e}^{-t}] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+2 z \left (t \right )+{\mathrm e}^{-t}-3 t, y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{-t}+t, z^{\prime }\left (t \right ) = -2 x \left (t \right )+5 y \left (t \right )+6 z \left (t \right )+2 \,{\mathrm e}^{-t}-t] \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime }-f \left (x \right ) \left (y-g \left (x \right )\right ) \sqrt {\left (y-a \right ) \left (y-b \right )} = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left (B x y+A \,x^{2}+a x +b y+c \right ) y^{\prime }-B g \left (x \right )^{2}+A x y+\alpha x +\beta y+\gamma = 0 \]

\[ {}\left (-1+x^{2} y\right ) y^{\prime }+8 x y^{2}-8 = 0 \]

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

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

\[ {}\left (\frac {\operatorname {e1} \left (x +a \right )}{\left (\left (x +a \right )^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {\operatorname {e2} \left (x -a \right )}{\left (\left (x -a \right )^{2}+y^{2}\right )^{\frac {3}{2}}}\right ) y^{\prime }-y \left (\frac {\operatorname {e1}}{\left (\left (x +a \right )^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {\operatorname {e2}}{\left (\left (x -a \right )^{2}+y^{2}\right )^{\frac {3}{2}}}\right ) = 0 \]

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

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

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

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

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

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

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

\[ {}\operatorname {d0} \left (x \right ) {y^{\prime }}^{2}+2 \operatorname {b0} \left (x \right ) y y^{\prime }+\operatorname {c0} \left (x \right ) y^{2}+2 \operatorname {d0} \left (x \right ) y^{\prime }+2 \operatorname {e0} \left (x \right ) y+\operatorname {f0} \left (x \right ) = 0 \]

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