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

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

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

\[ {}x^{\prime \prime }+\omega _{0}^{2} x = a \cos \left (\omega t \right ) \]

\[ {}f^{\prime \prime }+2 f^{\prime }+5 f = 0 \]

\[ {}f^{\prime \prime }+2 f^{\prime }+5 f = {\mathrm e}^{-t} \cos \left (3 t \right ) \]

\[ {}f^{\prime \prime }+6 f^{\prime }+9 f = {\mathrm e}^{-t} \]

\[ {}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t} \]

\[ {}f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t} \]

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 4 \,{\mathrm e}^{-x} \]

\[ {}y^{\prime \prime \prime }-12 y^{\prime }+16 y = 32 x -8 \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y = 0 \]

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

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

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

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

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

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

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

\[ {}\left (z^{2}+5 z +7\right ) y^{\prime \prime }+2 y = 0 \]

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

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

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

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

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

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

\[ {}y^{\prime } = \frac {y}{\ln \relax (x ) x} \]

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

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

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

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

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

\[ {}y^{\prime } = \frac {x^{2} y-32}{-x^{2}+16}+32 \]

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

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

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

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

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

\[ {}y^{\prime }-y = {\mathrm e}^{2 x} \]

\[ {}x^{2} y^{\prime }-4 x y = x^{7} \sin \relax (x ) \]

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

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

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

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

\[ {}y^{\prime }+\frac {y}{\ln \relax (x ) x} = 9 x^{2} \]

\[ {}y^{\prime }-y \tan \relax (x ) = 8 \left (\sin ^{3}\relax (x )\right ) \]

\[ {}x^{\prime } t +2 x = 4 \,{\mathrm e}^{t} \]

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

\[ {}1-y \sin \relax (x )-\cos \relax (x ) y^{\prime } = 0 \]

\[ {}y^{\prime }-\frac {y}{x} = 2 x^{2} \ln \relax (x ) \]

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

\[ {}y^{\prime }+\frac {m}{x} = \ln \relax (x ) \]

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

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

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

\[ {}x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y \]

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

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

\[ {}x y^{\prime }+y \ln \relax (x ) = y \ln \relax (y) \]

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-25 y = 0 \]

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

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

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

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

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

\[ {}y^{\prime \prime }-9 y = 0 \]

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

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

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

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

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \relax (x ) \]

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

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

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

\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \]

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

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

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

\[ {}y^{\prime } = \frac {{\mathrm e}^{x}-\sin \relax (y)}{x \cos \relax (y)} \]

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

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

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