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

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

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

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

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

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

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

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

\[ {}\sec \left (y\right )^{2} y^{\prime } = \tan \left (y\right )+2 x \,{\mathrm e}^{x} \]

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

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

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

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

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

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

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

\[ {}\left (\cot \left (x \right )-2 y^{2}\right ) y^{\prime } = y^{3} \csc \left (x \right ) \sec \left (x \right ) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}s^{\prime } = t \ln \left (s^{2 t}\right )+8 t^{2} \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {2 a x}{-x^{3} y+2 a \,x^{3}+2 a y^{4} x^{3}-16 y^{2} a^{2} x^{2}+32 a^{3} x +2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \]

\[ {}y^{\prime } = \frac {2 y^{6} \left (1+4 x y^{2}+y^{2}\right )}{y^{3}+4 y^{5} x +y^{5}+2+24 x y^{2}+96 x^{2} y^{4}+128 x^{3} y^{6}} \]

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

\[ {}y^{\left (5\right )}+a \,x^{\nu } y^{\prime }+a \nu \,x^{\nu -1} y = 0 \]

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

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

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

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

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

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

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

\[ {}\left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )^{3}+32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3} = 0 \]

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

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

\[ {}y^{\prime } = a \,{\mathrm e}^{k x} y^{2}+b y+c \,{\mathrm e}^{k n x}+d \,{\mathrm e}^{k \left (2 n +1\right ) x} \]

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