| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime } = {\mathrm e}^{y} y^{\prime }
\]
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| \[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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| \[
{} y^{\prime } = \frac {x^{2}+y^{2}}{x^{2}-y^{2}}
\]
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| \[
{} y^{\prime } = \frac {x^{2}+2 y^{2}}{x^{2}-2 y^{2}}
\]
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\]
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| \[
{} y y^{\prime \prime }+y^{\prime } = 0
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}}
\]
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| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \left (x^{2}-1\right )^{2}
\]
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| \[
{} \left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y = x \left (1+x \right )^{2}
\]
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| \[
{} -y+x y^{\prime }+\left (1-x \right ) y^{\prime \prime } = \left (1-x \right )^{2}
\]
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| \[
{} y-y^{\prime } \left (1+x \right )+x y^{\prime \prime } = x^{2} {\mathrm e}^{2 x}
\]
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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| \[
{} y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1} = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\]
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| \[
{} y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0
\]
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| \[
{} y^{\prime \prime }+\sin \left (y\right ) = 0
\]
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| \[
{} x y^{\prime } = y
\]
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| \[
{} x^{2} y^{\prime } = y
\]
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| \[
{} y^{\prime }-\frac {y}{x} = x^{2}
\]
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| \[
{} y^{\prime \prime }+2 x y^{\prime }-y = x
\]
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| \[
{} y^{\prime \prime }+y^{\prime }-x^{2} y = 1
\]
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| \[
{} x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 x y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0
\]
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| \[
{} x^{3} y^{\prime \prime }+\sin \left (x \right ) y = 0
\]
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| \[
{} x^{4} y^{\prime \prime }+\sin \left (x \right ) y = 0
\]
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| \[
{} x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 x y = 0
\]
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| \[
{} x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 x y = 0
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\]
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| \[
{} \left (x -1\right )^{2} y^{\prime \prime }-3 \left (x -1\right ) y^{\prime }+2 y = 0
\]
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| \[
{} 3 \left (1+x \right )^{2} y^{\prime \prime }-y^{\prime } \left (1+x \right )-y = 0
\]
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| \[
{} \left (-{\mathrm e}^{x}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{2}+y \,{\mathrm e}^{x} = 0
\]
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| \[
{} y^{\prime \prime }+2 x y = x^{2}
\]
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| \[
{} y^{\prime \prime }-x y^{\prime }+y = x
\]
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| \[
{} y^{\prime \prime }+y^{\prime }+y = x^{3}-x
\]
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| \[
{} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\left (x +2\right ) y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (1+x \right ) y = 0
\]
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| \[
{} 4 x^{2} y^{\prime \prime }+4 x^{2} y^{\prime }+2 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y = 0
\]
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| \[
{} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+x y = 0
\]
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| \[
{} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (x -1\right ) y = 0
\]
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| \[
{} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-x y = 0
\]
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| \[
{} x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\]
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| \[
{} 9 \left (x -2\right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (x -2\right ) y^{\prime }+16 y = 0
\]
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| \[
{} L i^{\prime }+R i = E_{0} \operatorname {Heaviside}\left (t \right )
\]
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| \[
{} i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right .
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )-4 z \left (t \right ), z^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )+z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )+1, y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 1+t y \left (t \right ), y^{\prime }\left (t \right ) = -t x \left (t \right )+y \left (t \right )]
\]
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| \[
{} y^{\prime } = -x +y^{2}
\]
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| \[
{} y^{\prime } = y+x \,{\mathrm e}^{y}
\]
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| \[
{} \left (x -1\right ) y^{\prime \prime }+y^{\prime } = 0
\]
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| \[
{} y^{\prime \prime }-x y = 1
\]
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| \[
{} y^{\prime \prime }-4 x y^{\prime }-4 y = {\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }+5 x y^{\prime }+y \sqrt {x} = 0
\]
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| \[
{} x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0
\]
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| \[
{} x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y = 0
\]
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| \[
{} x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0
\]
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| \[
{} x^{3} y^{\prime \prime }+y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\]
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| \[
{} y^{\prime \prime }-x^{2} y = 0
\]
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| \[
{} \left ({\mathrm e}^{x}-1-x \right ) y^{\prime \prime }+x y = 0
\]
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| \[
{} y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 10 x^{3}-2 x +5
\]
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| \[
{} y+y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right .
\]
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| \[
{} y+y^{\prime } = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\]
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| \[
{} y+y^{\prime } = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\]
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| \[
{} 2 y^{\prime \prime }+t y^{\prime }-2 y = 10
\]
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| \[
{} y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right )
\]
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| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right )-9 z \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = 10 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )+z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right )+{\mathrm e}^{-t} \sin \left (2 t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+9 z \left (t \right )+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ), z^{\prime }\left (t \right ) = y \left (t \right )+6 z \left (t \right )-{\mathrm e}^{-t}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 7 x \left (t \right )+5 y \left (t \right )-9 z \left (t \right )-8 \,{\mathrm e}^{-2 t}, y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{5 t}, z^{\prime }\left (t \right ) = -2 y \left (t \right )+3 z \left (t \right )+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+2 z \left (t \right )+{\mathrm e}^{-t}-3 t, y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{-t}+t, z^{\prime }\left (t \right ) = -2 x \left (t \right )+5 y \left (t \right )+6 z \left (t \right )+2 \,{\mathrm e}^{-t}-t]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = \frac {9 x \left (t \right )}{10}+\frac {21 y \left (t \right )}{10}+\frac {16 z \left (t \right )}{5}, y^{\prime }\left (t \right ) = \frac {7 x \left (t \right )}{10}+\frac {13 y \left (t \right )}{2}+\frac {21 z \left (t \right )}{5}, z^{\prime }\left (t \right ) = \frac {11 x \left (t \right )}{10}+\frac {17 y \left (t \right )}{10}+\frac {17 z \left (t \right )}{5}\right ]
\]
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| \[
{} \left [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{3} \left (t \right )-\frac {9 x_{4} \left (t \right )}{5}, x_{2}^{\prime }\left (t \right ) = \frac {51 x_{2} \left (t \right )}{10}-x_{4} \left (t \right )+3 x_{5} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{2} \left (t \right )-\frac {31 x_{3} \left (t \right )}{10}+4 x_{4} \left (t \right ), x_{5}^{\prime }\left (t \right ) = -\frac {14 x_{1} \left (t \right )}{5}+\frac {3 x_{4} \left (t \right )}{2}-x_{5} \left (t \right )\right ]
\]
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| \[
{} \left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2} = 4 x^{2} y^{2}
\]
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| \[
{} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\]
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| \[
{} 4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\]
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| \[
{} 4 y^{3} {y^{\prime }}^{2}+4 x y^{\prime }+y = 0
\]
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| \[
{} {y^{\prime }}^{3}+x {y^{\prime }}^{2}-y = 0
\]
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| \[
{} y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0
\]
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| \[
{} 2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4} = 0
\]
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| \[
{} x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y = 0
\]
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| \[
{} y^{\prime } \left (x y^{\prime }-y+k \right )+a = 0
\]
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| \[
{} x^{6} {y^{\prime }}^{3}-3 x y^{\prime }-3 y = 0
\]
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| \[
{} y = x^{6} {y^{\prime }}^{3}-x y^{\prime }
\]
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| \[
{} {y^{\prime }}^{4} x -2 {y^{\prime }}^{3} y+12 x^{3} = 0
\]
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| \[
{} x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0
\]
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| \[
{} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\]
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| \[
{} 2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0
\]
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| \[
{} 2 {y^{\prime }}^{2}+x y^{\prime }-2 y = 0
\]
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| \[
{} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\]
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| \[
{} 4 x {y^{\prime }}^{2}-3 y y^{\prime }+3 = 0
\]
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| \[
{} {y^{\prime }}^{3}-x y^{\prime }+2 y = 0
\]
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| \[
{} 5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0
\]
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| \[
{} 2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y = 0
\]
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| \[
{} 5 {y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\]
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| \[
{} {y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\]
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