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\[
{} y^{2} \left (x^{2} y^{\prime \prime }-x y^{\prime }+y\right ) = x^{3}
\]
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\[
{} x^{2} y^{2} y^{\prime \prime }-3 x y^{2} y^{\prime }+4 y^{3}+x^{6} = 0
\]
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\[
{} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2} = 0
\]
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\[
{} x \left (x^{2} y^{\prime }+2 x y\right ) y^{\prime \prime }+4 x {y^{\prime }}^{2}+8 x y y^{\prime }+4 y^{2}-1 = 0
\]
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\[
{} x \left (1+x y\right ) y^{\prime \prime }+x^{2} {y^{\prime }}^{2}+\left (4 x y+2\right ) y^{\prime }+y^{2}+1 = 0
\]
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\[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-{y^{\prime }}^{4} = 0
\]
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\[
{} a^{2} y^{\prime \prime } = 2 x \sqrt {1+{y^{\prime }}^{2}}
\]
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\[
{} x^{2} y y^{\prime \prime }+x^{2} {y^{\prime }}^{2}-5 x y y^{\prime } = 4 y^{2}
\]
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\[
{} y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\]
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\[
{} 5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime } = 0
\]
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\[
{} 40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )} = 0
\]
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\[
{} {y^{\prime \prime }}^{2}+2 x y^{\prime \prime }-y^{\prime } = 0
\]
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\[
{} {y^{\prime \prime }}^{2}-2 x y^{\prime \prime }-y^{\prime } = 0
\]
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\[
{} 2 x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+12 x y^{\prime }-12 y = 0
\]
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\[
{} y^{\prime \prime \prime }-\frac {3 y^{\prime \prime }}{x}+\frac {6 y^{\prime }}{x^{2}}-\frac {6 y}{x^{3}} = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y = 0
\]
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\[
{} y^{\prime \prime } \sin \left (x \right )^{2} = 2 y
\]
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\[
{} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0
\]
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\[
{} x y^{\prime \prime \prime }-y^{\prime \prime }+x y^{\prime }-y = 0
\]
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\[
{} \left (-x^{2}+1\right ) y^{\prime \prime \prime }-x y^{\prime \prime }+y^{\prime } = 0
\]
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\[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 2 x^{3}
\]
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\[
{} y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x} = x -1
\]
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\[
{} \left (x^{2}+2\right ) y^{\prime \prime \prime }-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime }-2 x y = x^{4}+12
\]
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\[
{} y^{\prime \prime \prime }+y^{\prime } = 0
\]
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\[
{} y^{\prime \prime }+y = 0
\]
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\[
{} y^{\prime \prime }+\frac {y}{\ln \left (x \right ) x^{2}} = {\mathrm e}^{x} \left (\frac {2}{x}+\ln \left (x \right )\right )
\]
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\[
{} y^{\prime \prime }+p_{1} y^{\prime }+p_{2} y = 0
\]
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\[
{} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0
\]
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\[
{} y^{\prime \prime } \sin \left (x \right )^{2}+\sin \left (x \right ) \cos \left (x \right ) y^{\prime } = y
\]
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\[
{} y^{\prime \prime \prime \prime }-2 y^{\prime \prime } = 0
\]
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\[
{} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0
\]
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\[
{} y^{\prime \prime \prime \prime }+4 y = 0
\]
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\[
{} y^{\prime \prime \prime \prime }-y = 0
\]
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\[
{} 2 y^{\prime \prime }+y^{\prime }-y = 0
\]
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\[
{} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y = 0
\]
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\[
{} y^{\prime \prime }-4 y^{\prime }+4 y = x^{2}
\]
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\[
{} y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{x}+{\mathrm e}^{2 x}
\]
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\[
{} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = x \,{\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = \left (1+x \right ) {\mathrm e}^{x}
\]
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\[
{} y^{\prime \prime }+4 y = \sin \left (2 x \right ) x
\]
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\[
{} y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )
\]
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\[
{} y^{\prime \prime }-y = \frac {{\mathrm e}^{x}-{\mathrm e}^{-x}}{{\mathrm e}^{x}+{\mathrm e}^{-x}}
\]
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\[
{} y^{\prime \prime }-2 y = 4 x^{2} {\mathrm e}^{x^{2}}
\]
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\[
{} y^{\prime \prime }+y = \sin \left (x \right ) \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }+9 y = \ln \left (2 \sin \left (\frac {x}{2}\right )\right )
\]
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\[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {n \left (n +1\right ) y}{x^{2}} = 0
\]
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\[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x
\]
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\[
{} x^{2} y^{\prime \prime }-x y^{\prime }+2 y = x \ln \left (x \right )
\]
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\[
{} x^{2} y^{\prime \prime }-2 y = x^{2}+\frac {1}{x}
\]
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\[
{} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = x^{3}+3 x
\]
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\[
{} \left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 4 \cos \left (\ln \left (1+x \right )\right )
\]
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\[
{} y^{\prime \prime }-\frac {y^{\prime }}{x}+\left (1-\frac {m^{2}}{x^{2}}\right ) y = 0
\]
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\[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y = 0
\]
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\[
{} y^{\prime \prime }+\frac {2 p y^{\prime }}{x}+y = 0
\]
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\[
{} x y^{\prime \prime }-y^{\prime }-x^{3} y = 0
\]
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\[
{} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right )
\]
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\[
{} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {y \left (-8+\sqrt {x}+x \right )}{4 x^{2}} = 0
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )]
\]
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\[
{} [y^{\prime }\left (x \right ) = y \left (x \right )+z \left (x \right ), z^{\prime }\left (x \right ) = y \left (x \right )+z \left (x \right )+x]
\]
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\[
{} \left [y^{\prime }\left (x \right ) = \frac {y \left (x \right )^{2}}{z \left (x \right )}, z^{\prime }\left (x \right ) = \frac {y \left (x \right )}{2}\right ]
\]
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\[
{} \left [y^{\prime }\left (x \right ) = 1-\frac {1}{z \left (x \right )}, z^{\prime }\left (x \right ) = \frac {1}{y \left (x \right )-x}\right ]
\]
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\[
{} [y^{\prime }\left (x \right ) = -z \left (x \right ), z^{\prime }\left (x \right ) = y \left (x \right )]
\]
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\[
{} y^{\prime \prime } = x +y^{2}
\]
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\[
{} y^{\prime \prime }+2 y^{\prime }+y^{2} = 0
\]
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\[
{} \left [y^{\prime }\left (x \right ) = \frac {z \left (x \right )^{2}}{y \left (x \right )}, z^{\prime }\left (x \right ) = \frac {y \left (x \right )^{2}}{z \left (x \right )}\right ]
\]
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\[
{} \left [y^{\prime }\left (x \right ) = \frac {y \left (x \right )^{2}}{z \left (x \right )}, z^{\prime }\left (x \right ) = \frac {z \left (x \right )^{2}}{y \left (x \right )}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right ) = t^{2}, y^{\prime }\left (t \right )+y \left (t \right )+z \left (t \right ) = 2 t, z^{\prime }\left (t \right )+z \left (t \right ) = t]
\]
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\[
{} [x^{\prime }\left (t \right )+5 x \left (t \right )+y \left (t \right ) = 7 \,{\mathrm e}^{t}-27, y^{\prime }\left (t \right )-2 x \left (t \right )+3 y \left (t \right ) = -3 \,{\mathrm e}^{t}+12]
\]
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\[
{} [y^{\prime \prime }\left (x \right )+z^{\prime }\left (x \right )-2 z \left (x \right ) = {\mathrm e}^{2 x}, z^{\prime }\left (x \right )+2 y^{\prime }\left (x \right )-3 y \left (x \right ) = 0]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+{\mathrm e}^{t}+{\mathrm e}^{-t}]
\]
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\[
{} \left [y^{\prime }\left (x \right )+\frac {2 z \left (x \right )}{x^{2}} = 1, z^{\prime }\left (x \right )+y \left (x \right ) = x\right ]
\]
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\[
{} [t x^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right ) = t, t y^{\prime }\left (t \right )-x \left (t \right )+y \left (t \right ) = 0]
\]
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\[
{} [t x^{\prime }\left (t \right )+6 x \left (t \right )-y \left (t \right )-3 z \left (t \right ) = 0, t y^{\prime }\left (t \right )+23 x \left (t \right )-6 y \left (t \right )-9 z \left (t \right ) = 0, t z^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right )-2 z \left (t \right ) = 0]
\]
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\[
{} [x^{\prime }\left (t \right )+5 x \left (t \right )+y \left (t \right ) = {\mathrm e}^{t}, y^{\prime }\left (t \right )+3 y \left (t \right )-x \left (t \right ) = {\mathrm e}^{2 t}]
\]
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\[
{} y^{\prime } = 2 x
\]
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\[
{} x y^{\prime } = 2 y
\]
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\[
{} y y^{\prime } = {\mathrm e}^{2 x}
\]
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\[
{} y^{\prime } = k y
\]
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\[
{} y^{\prime \prime }+4 y = 0
\]
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\[
{} y^{\prime \prime }-4 y = 0
\]
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\[
{} x y^{\prime }+y = y^{\prime } \sqrt {1-x^{2} y^{2}}
\]
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\[
{} x y^{\prime } = y+x^{2}+y^{2}
\]
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\[
{} y^{\prime } = \frac {x y}{x^{2}+y^{2}}
\]
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\[
{} 2 x y y^{\prime } = x^{2}+y^{2}
\]
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\[
{} x y^{\prime }+y = x^{4} {y^{\prime }}^{2}
\]
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\[
{} y^{\prime } = \frac {y^{2}}{x y-x^{2}}
\]
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\[
{} \left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime } = y
\]
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\[
{} 1+y^{2}+y^{2} y^{\prime } = 0
\]
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\[
{} y^{\prime } = {\mathrm e}^{3 x}-x
\]
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\[
{} x y^{\prime } = 1
\]
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\[
{} y^{\prime } = x \,{\mathrm e}^{x^{2}}
\]
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\[
{} y^{\prime } = \arcsin \left (x \right )
\]
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\[
{} \left (1+x \right ) y^{\prime } = x
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime } = x
\]
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\[
{} \left (x^{3}+1\right ) y^{\prime } = x
\]
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\[
{} \left (x^{2}+1\right ) y^{\prime } = \arctan \left (x \right )
\]
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\[
{} x y y^{\prime } = -1+y
\]
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\[
{} x^{5} y^{\prime }+y^{5} = 0
\]
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