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

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

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

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

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

\[ {}x \left (2-9 y^{2} x \right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime } = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 1+3 x \]

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{2 x} \]

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

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

\[ {}p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u = f \left (x \right ) \]

\[ {}\sin \left (x \right ) u^{\prime \prime }+2 \cos \left (x \right ) u^{\prime }+\sin \left (x \right ) u = 0 \]

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

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

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

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

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 \sin \left (t \right )-5 \cos \left (t \right ) \]

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

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

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

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

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

\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 50 \,{\mathrm e}^{2 x} \]

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 50 \,{\mathrm e}^{2 x} \]

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

\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \sin \left (3 x \right ) \]

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

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

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

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

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

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

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

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

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

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

\[ {}\phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right ) = 0 \]

\[ {}u^{\prime \prime }-\cot \left (\theta \right ) u^{\prime } = 0 \]

\[ {}\left (\phi ^{\prime }-\frac {\phi ^{2}}{2}\right ) \sin \left (\theta \right )^{2}-\phi \sin \left (\theta \right ) \cos \left (\theta \right ) = \frac {\cos \left (2 \theta \right )}{2}+1 \]

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

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

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

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

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0 \]

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

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

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

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

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

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

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

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

\[ {}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-18 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-9 x_{2} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+3 x_{2} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+5 x_{2} \left (t \right )] \]