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\[
{} [y_{1}^{\prime }\left (x \right ) = 2 x y_{1} \left (x \right )-x^{2} y_{2} \left (x \right )+4 x, y_{2}^{\prime }\left (x \right ) = {\mathrm e}^{x} y_{1} \left (x \right )+3 \,{\mathrm e}^{-x} y_{2} \left (x \right )-\cos \left (3 x \right )]
\]
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\[
{} S^{\prime } = S^{3}-2 S^{2}+S
\]
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\[
{} S^{\prime } = S^{3}-2 S^{2}+S
\]
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\[
{} S^{\prime } = S^{3}-2 S^{2}+S
\]
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\[
{} y^{\prime } = {\mathrm e}^{\frac {2}{y}}
\]
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\[
{} y^{\prime } = {\mathrm e}^{\frac {2}{y}}
\]
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\[
{} y^{\prime } = 2 y^{3}+t^{2}
\]
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\[
{} y^{\prime } = \cos \left (y\right )
\]
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\[
{} w^{\prime } = w \cos \left (w\right )
\]
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\[
{} w^{\prime } = w \cos \left (w\right )
\]
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\[
{} w^{\prime } = w \cos \left (w\right )
\]
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\[
{} y^{\prime } = \left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right )
\]
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\[
{} y^{\prime } = \left (y-1\right ) \left (y-2\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right )
\]
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\[
{} y^{2} y^{\prime \prime } = 8 x^{2}
\]
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\[
{} \sin \left (x +y\right )-y y^{\prime } = 0
\]
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\[
{} y^{2} y^{\prime }+3 x^{2} y = \sin \left (x \right )
\]
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\[
{} y^{\prime \prime } = 2 y y^{\prime }
\]
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\[
{} y^{\prime \prime } = 2 y y^{\prime }
\]
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\[
{} y^{\prime \prime }+x^{2} y^{\prime }+4 y = y^{3}
\]
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\[
{} y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime } = y
\]
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\[
{} x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y = 0
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )-5]
\]
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\[
{} y y^{\prime }+y^{4} = \sin \left (x \right )
\]
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\[
{} x {y^{\prime \prime }}^{2}+2 y = 2 x
\]
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\[
{} x^{\prime \prime }+2 \sin \left (x\right ) = \sin \left (2 t \right )
\]
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\[
{} 4 x \left (x^{2}+y^{2}\right )-5 y+4 y \left (x^{2}+y^{2}-5 x \right ) y^{\prime } = 0
\]
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\[
{} y^{\prime }+t^{2} = \frac {1}{y^{2}}
\]
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\[
{} 1 = \cos \left (y\right ) y^{\prime }
\]
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\[
{} 1-y^{2} \cos \left (t y\right )+\left (t y \cos \left (t y\right )+\sin \left (t y\right )\right ) y^{\prime } = 0
\]
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\[
{} {\mathrm e}^{y}-2 t y+\left (t \,{\mathrm e}^{y}-t^{2}\right ) y^{\prime } = 0
\]
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\[
{} \frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime } = 0
\]
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\[
{} \frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime } = 0
\]
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\[
{} y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime } = \sqrt {x -y}
\]
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\[
{} y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0
\]
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\[
{} {y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2} = 0
\]
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\[
{} {y^{\prime \prime }}^{2}-2 y^{\prime \prime } y^{\prime }+y^{2} = 0
\]
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\[
{} y^{\prime } = \sin \left (y\right )-\cos \left (x \right )
\]
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\[
{} y \ln \left (y\right )+x y^{\prime } = 1
\]
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\[
{} x^{2} y^{\prime } \cos \left (y\right )+1 = 0
\]
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\[
{} x^{2} y^{\prime }+\cos \left (2 y\right ) = 1
\]
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\[
{} x^{3} y^{\prime }-\sin \left (y\right ) = 1
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2} = 0
\]
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\[
{} x^{2} y^{\prime }+\sin \left (2 y\right ) = 1
\]
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\[
{} \frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime } = 0
\]
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\[
{} 3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime } = 0
\]
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\[
{} \frac {y+\sin \left (x \right ) \cos \left (x y\right )^{2}}{\cos \left (x y\right )^{2}}+\left (\frac {x}{\cos \left (x y\right )^{2}}+\sin \left (y\right )\right ) y^{\prime } = 0
\]
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\[
{} {y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0
\]
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\[
{} 8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2} = 27 y-27 x
\]
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\[
{} y^{\prime \prime } = y^{\prime } \ln \left (y^{\prime }\right )
\]
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\[
{} y^{\prime \prime } = 2 y y^{\prime }
\]
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\[
{} 3 y^{\prime } y^{\prime \prime } = 2 y
\]
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\[
{} y^{\prime \prime \prime } = 3 y y^{\prime }
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 8 \,{\mathrm e}^{x}+9
\]
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\[
{} y^{\prime \prime }+4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right )
\]
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\[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right )
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right )
\]
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\[
{} 2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y = \frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}}
\]
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\[
{} x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x = 0
\]
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\[
{} x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x = 0
\]
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\[
{} x^{\prime \prime }-x^{\prime }+x-x^{2} = 0
\]
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\[
{} y^{\prime \prime }+y = 0
\]
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\[
{} y^{\prime \prime }+\alpha ^{2} y = 1
\]
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\[
{} \ln \left (x \right ) y^{\prime \prime }-\sin \left (x \right ) y = 0
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \frac {y \left (t \right )+t}{x \left (t \right )+y \left (t \right )}, y^{\prime }\left (t \right ) = \frac {t +x \left (t \right )}{x \left (t \right )+y \left (t \right )}\right ]
\]
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\[
{} [x^{\prime \prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right ) x^{\prime }\left (t \right )+x \left (t \right )]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = \cos \left (x \left (t \right )\right )^{2} \cos \left (y \left (t \right )\right )^{2}+\sin \left (x \left (t \right )\right )^{2} \cos \left (y \left (t \right )\right )^{2}, y^{\prime }\left (t \right ) = -\frac {\sin \left (2 x \left (t \right )\right ) \sin \left (2 y \left (t \right )\right )}{2}\right ]
\]
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\[
{} \sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime } = \sqrt {1-t^{2}-y^{2}}
\]
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\[
{} y^{\prime } = \frac {\ln \left (t y\right )}{1-t^{2}+y^{2}}
\]
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\[
{} y^{\prime } = \left (t^{2}+y^{2}\right )^{{3}/{2}}
\]
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\[
{} {\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0
\]
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\[
{} \frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime } = 0
\]
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\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+4, y^{\prime }\left (t \right ) = -2 x \left (t \right )+\sin \left (t \right ) y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 2-y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = \frac {y \left (t \right )}{2}-\frac {y \left (t \right )^{2}}{4}-\frac {3 x \left (t \right ) y \left (t \right )}{4}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = -\left (x \left (t \right )-y \left (t \right )\right ) \left (1-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = x \left (t \right ) \left (2+y \left (t \right )\right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ) \left (2-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right )-2 x \left (t \right ) y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = \left (2+x \left (t \right )\right ) \left (-x \left (t \right )+y \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )^{2}-y \left (t \right )^{2}]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-\frac {x \left (t \right )^{3}}{5}-\frac {y \left (t \right )}{5}\right ]
\]
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\[
{} \left [x^{\prime }\left (t \right ) = x \left (t \right ) \left (1-x \left (t \right )-y \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (\frac {3}{4}-y \left (t \right )-\frac {x \left (t \right )}{2}\right )\right ]
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y+y^{3} = 0
\]
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\[
{} y^{\prime \prime }+\mu \left (1-y^{2}\right ) y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+3 y \ln \left (t \right ) = 0
\]
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\[
{} \left (x +3\right ) y^{\prime \prime }+x y^{\prime }+y \ln \left (x \right ) = 0
\]
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\[
{} \left (x -2\right ) y^{\prime \prime }+y^{\prime }+\left (x -2\right ) \tan \left (x \right ) y = 0
\]
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\[
{} y^{\prime \prime }+y+\frac {y^{3}}{5} = \cos \left (w t \right )
\]
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\[
{} y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5} = \cos \left (w t \right )
\]
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\[
{} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y = \cos \left (t \right )
\]
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\[
{} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y = 0
\]
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\[
{} y^{\prime \prime \prime }+t y^{\prime \prime }+t^{2} y^{\prime }+t^{2} y = \ln \left (t \right )
\]
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\[
{} \left (x -4\right ) y^{\prime \prime \prime \prime }+\left (1+x \right ) y^{\prime \prime }+\tan \left (x \right ) y = 0
\]
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\[
{} \left (x^{2}-2\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+3 y = 0
\]
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\[
{} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y = \cos \left (t \right )
\]
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\[
{} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y = 0
\]
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\[
{} y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 t^{3} y = \ln \left (t \right )
\]
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\[
{} \left (x -1\right ) y^{\prime \prime \prime \prime }+\left (x +5\right ) y^{\prime \prime }+\tan \left (x \right ) y = 0
\]
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\[
{} \left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y = 0
\]
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\[
{} y = 2 x y^{\prime }+\frac {x^{2}}{2}+{y^{\prime }}^{2}
\]
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\[
{} y = \frac {k \left (x +y y^{\prime }\right )}{\sqrt {1+{y^{\prime }}^{2}}}
\]
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