| # | ODE | Mathematica | Maple | Sympy |
| \[
{} [y^{\prime \prime }\left (t \right ) = x \left (t \right ), y^{\prime \prime }\left (t \right ) = y \left (t \right )]
\]
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| \[
{} [y^{\prime \prime }\left (t \right ) = x \left (t \right )-2, y^{\prime \prime }\left (t \right ) = y \left (t \right )+2]
\]
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| \[
{} [y^{\prime }\left (t \right )+6 y \left (t \right ) = x^{\prime }\left (t \right ), 3 x \left (t \right )-x^{\prime }\left (t \right ) = 2 y^{\prime }\left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right ) = 1, 2 x \left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = t]
\]
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| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right ) = -\sin \left (t \right ), x^{\prime }\left (t \right )-3 x \left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right ) = 4 \cos \left (t \right )]
\]
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| \[
{} [x^{\prime \prime }\left (t \right )+2 y^{\prime }\left (t \right )+8 x \left (t \right ) = 32 t, y^{\prime \prime }\left (t \right )+3 x^{\prime }\left (t \right )-2 y \left (t \right ) = 60 \,{\mathrm e}^{-t}]
\]
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| \[
{} \left [x^{\prime }\left (t \right )-2 y^{\prime }\left (t \right ) = {\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right ) = \sqrt {t}\right ]
\]
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| \[
{} [x^{\prime }\left (t \right )+3 y^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right ), 3 x^{\prime }\left (t \right )-y^{\prime }\left (t \right ) = \sin \left (t \right )]
\]
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| \[
{} [r^{\prime \prime }\left (t \right ) = r \left (t \right )+y \left (t \right ), y^{\prime \prime }\left (t \right ) = 5 r \left (t \right )-3 y \left (t \right )+t^{2}]
\]
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| \[
{} [x \left (t \right ) y^{\prime }\left (t \right )+y \left (t \right ) x^{\prime }\left (t \right ) = t^{2}, 2 x^{\prime \prime }\left (t \right )-y^{\prime }\left (t \right ) = 5 t]
\]
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| \[
{} [x^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right ) = y \left (t \right )+\sin \left (t \right ), y^{\prime \prime }\left (t \right )+x^{\prime }\left (t \right )-y \left (t \right ) = 2 t^{2}-x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = 2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ) z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right ) z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 1+y \left (t \right )^{2}, z^{\prime }\left (t \right ) = z \left (t \right )]
\]
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| \[
{} [t^{2} y^{\prime \prime }\left (t \right )+t z^{\prime }\left (t \right )+z \left (t \right ) = t, t y^{\prime }\left (t \right )+z \left (t \right ) = \ln \left (t \right )]
\]
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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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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right )+x \left (t \right )-5 y \left (t \right ) = 0, y^{\prime }\left (t \right )+4 x \left (t \right )+5 y \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )+3 y^{\prime }\left (t \right )+y \left (t \right ) = {\mathrm e}^{t}, -x \left (t \right )+y^{\prime }\left (t \right ) = y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right )-3 x \left (t \right )-6 y \left (t \right ) = 27 t^{2}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 y \left (t \right ) = 5 \,{\mathrm e}^{t}]
\]
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| \[
{} [x^{\prime \prime }\left (t \right ) = -2 y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-x^{\prime }\left (t \right )]
\]
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| \[
{} [y^{\prime \prime }\left (t \right ) = x \left (t \right )-2, x^{\prime \prime }\left (t \right ) = y \left (t \right )+2]
\]
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| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right ) = \cos \left (t \right ), x \left (t \right )+y^{\prime \prime }\left (t \right ) = 2]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = 2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+5 y \left (t \right )+3 z \left (t \right ), z^{\prime }\left (t \right ) = 3 x \left (t \right )+9 y \left (t \right )+5 z \left (t \right )]
\]
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| \[
{} [x^{\prime \prime }\left (t \right ) = y \left (t \right )+4 \,{\mathrm e}^{-2 t}, y^{\prime \prime }\left (t \right ) = x \left (t \right )-{\mathrm e}^{-2 t}]
\]
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| \[
{} [x^{\prime }\left (t \right )+6 x \left (t \right )+3 y^{\prime }\left (t \right )+2 y \left (t \right ) = 0, x^{\prime }\left (t \right )+5 x \left (t \right )+2 y^{\prime }\left (t \right )+3 y \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )-x \left (t \right )+2 y^{\prime }\left (t \right )+7 y \left (t \right ) = 0, 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+5 y \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )+5 x \left (t \right )+3 y^{\prime }\left (t \right )-11 y \left (t \right ) = 0, x^{\prime }\left (t \right )+3 x \left (t \right )+y^{\prime }\left (t \right )-7 y \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )-2 x \left (t \right )+4 y \left (t \right ) = 0, 3 x \left (t \right )+2 y^{\prime }\left (t \right )+y \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )+3 x \left (t \right )+2 y \left (t \right ) = 0, 3 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )+4 x \left (t \right )+3 y^{\prime }\left (t \right )+4 y \left (t \right ) = 0, x^{\prime }\left (t \right )+2 x \left (t \right )+2 y^{\prime }\left (t \right )+2 y \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )+x \left (t \right )+2 y^{\prime }\left (t \right )+3 y \left (t \right ) = 0, x^{\prime }\left (t \right )-2 x \left (t \right )+5 y^{\prime }\left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = 0, 5 x \left (t \right )+y^{\prime }\left (t \right )-3 y \left (t \right ) = 0]
\]
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| \[
{} [2 x \left (t \right )-y^{\prime }\left (t \right )-5 y \left (t \right ) = 0, x^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right ) = 0]
\]
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| \[
{} [2 x^{\prime }\left (t \right )-6 x \left (t \right )+3 y^{\prime }\left (t \right )-2 y \left (t \right ) = 0, 7 x^{\prime }\left (t \right )+4 x \left (t \right )+7 y^{\prime }\left (t \right )+20 y \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right ) = 8, 2 x \left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = 2 \,{\mathrm e}^{-t}-8]
\]
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| \[
{} [x^{\prime }\left (t \right )+2 y \left (t \right ) = 4 \,{\mathrm e}^{2 t}, x \left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = 2 \,{\mathrm e}^{2 t}]
\]
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| \[
{} [x^{\prime }\left (t \right )-x \left (t \right )+2 y^{\prime }\left (t \right )+7 y \left (t \right ) = 3 t -15, 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+5 y \left (t \right ) = 9 t -7]
\]
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| \[
{} [x^{\prime }\left (t \right )+3 x \left (t \right )-y^{\prime }\left (t \right )-y \left (t \right ) = 0, 2 x^{\prime }\left (t \right )-9 x \left (t \right )+y^{\prime }\left (t \right )+4 y \left (t \right ) = 15 \,{\mathrm e}^{-3 t}]
\]
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| \[
{} [3 x \left (t \right )-y^{\prime }\left (t \right )-2 y \left (t \right ) = 8 t, x^{\prime }\left (t \right )-2 x \left (t \right )+y \left (t \right ) = 16 \,{\mathrm e}^{-t}]
\]
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| \[
{} [2 x^{\prime }\left (t \right )-x \left (t \right )-y^{\prime }\left (t \right )+y \left (t \right ) = 4 t \,{\mathrm e}^{-t}-3 \,{\mathrm e}^{-t}, x^{\prime }\left (t \right )+4 x \left (t \right )-2 y^{\prime }\left (t \right )-4 y \left (t \right ) = 2 t \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{-t}]
\]
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| \[
{} [2 x^{\prime }\left (t \right )-x \left (t \right )+7 y^{\prime }\left (t \right )+3 y \left (t \right ) = 90 \sin \left (2 t \right ), x^{\prime }\left (t \right )-5 x \left (t \right )+8 y^{\prime }\left (t \right )-3 y \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime \prime }\left (t \right ) = y \left (t \right )+4 \,{\mathrm e}^{-2 t}, y^{\prime \prime }\left (t \right ) = x \left (t \right )-{\mathrm e}^{-2 t}]
\]
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| \[
{} [x^{\prime }\left (t \right )-5 x \left (t \right )+y^{\prime }\left (t \right )+2 z \left (t \right ) = 24 \,{\mathrm e}^{-t}, x^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = 0, 5 y^{\prime }\left (t \right )-11 y \left (t \right )+2 z^{\prime }\left (t \right )-2 z \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )+3 x \left (t \right )-2 y \left (t \right ) = {\mathrm e}^{-t}, y^{\prime }\left (t \right )-x \left (t \right )+4 y \left (t \right ) = \sin \left (2 t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right )-x \left (t \right )+2 y \left (t \right )-z \left (t \right ) = t^{2}, y^{\prime }\left (t \right )+3 x \left (t \right )-y \left (t \right )+4 z \left (t \right ) = {\mathrm e}^{t}, z^{\prime }\left (t \right )-2 x \left (t \right )+y \left (t \right )-z \left (t \right ) = 0]
\]
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| \[
{} [z \left (t \right )+x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right )-2 x \left (t \right ) = y \left (t \right )+3 t, z^{\prime }\left (t \right )+4 y \left (t \right ) = z \left (t \right )-\cos \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right )+5 x \left (t \right )-4 y \left (t \right ) = 0, y^{\prime }\left (t \right )-x \left (t \right )+2 y \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )+x \left (t \right )-5 y \left (t \right ) = 0, y^{\prime }\left (t \right )+4 x \left (t \right )+5 y \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )-2 x \left (t \right )+3 y \left (t \right ) = 0, -2 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )+3 x \left (t \right )-6 y \left (t \right ) = 0, y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+8 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-7 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -12 x \left (t \right )-7 y \left (t \right ), y^{\prime }\left (t \right ) = 19 x \left (t \right )+11 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right )-y \left (t \right ) = t, x \left (t \right )+y^{\prime }\left (t \right ) = t^{2}]
\]
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| \[
{} [x^{\prime }\left (t \right )+3 x \left (t \right )+4 y \left (t \right ) = 8 \,{\mathrm e}^{t}, -x \left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )-2 x \left (t \right )+y \left (t \right ) = {\mathrm e}^{-t}, y^{\prime }\left (t \right )-3 x \left (t \right )+2 y \left (t \right ) = t]
\]
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| \[
{} [x^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right ) = 100 \sin \left (t \right ), y^{\prime }\left (t \right )-4 x \left (t \right )-y \left (t \right ) = 36 t]
\]
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| \[
{} [x^{\prime }\left (t \right )-3 x \left (t \right )-6 y \left (t \right ) = 9-9 t, y^{\prime }\left (t \right )+3 x \left (t \right )+3 y \left (t \right ) = 9 t \,{\mathrm e}^{-3 t}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )+t \,{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )+{\mathrm e}^{-t}]
\]
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| \[
{} [x^{\prime }\left (t \right )+4 x \left (t \right )+2 y \left (t \right )-z \left (t \right ) = 12 \,{\mathrm e}^{t}, y^{\prime }\left (t \right )-2 x \left (t \right )-5 y \left (t \right )+3 z \left (t \right ) = 0, z^{\prime }\left (t \right )+4 x \left (t \right )+z \left (t \right ) = 30 \,{\mathrm e}^{-t}]
\]
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| \[
{} y y^{\prime } = x^{2}
\]
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| \[
{} y^{\prime } \left (1+x \right ) = 1+y
\]
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| \[
{} 1+y^{2} = \left (x^{2}+1\right ) y^{\prime }
\]
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| \[
{} y^{\prime } \sin \left (y\right ) = \sec \left (x \right )^{2}
\]
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| \[
{} x^{\prime } = \frac {x}{t}
\]
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| \[
{} y^{\prime } \left (-x^{2}+1\right ) = 1-y^{2}
\]
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| \[
{} \frac {\tan \left (y\right )}{\cos \left (x \right )} = \cos \left (x \right ) y^{\prime }
\]
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| \[
{} x y^{\prime } = \left (1+x \right ) y^{2}
\]
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| \[
{} x \cos \left (y\right ) y^{\prime }-\left (x^{2}+1\right ) \sin \left (y\right ) = 0
\]
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{} \left (x^{2}-1\right ) y^{\prime } = x \left (y-1\right )
\]
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| \[
{} x \left (y+2\right )+y \left (x +2\right ) y^{\prime } = 0
\]
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| \[
{} x y \left (x^{2}+1\right ) y^{\prime }-y^{2} = 1
\]
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| \[
{} x y^{\prime }+y = 0
\]
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| \[
{} x y^{\prime }+y-1 = 0
\]
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| \[
{} y-x y^{\prime } = 3 y^{2} y^{\prime }
\]
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| \[
{} 2 x y+x^{2} y^{\prime } = 0
\]
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| \[
{} x \cos \left (y\right ) y^{\prime }+\sin \left (y\right ) = 5
\]
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| \[
{} y^{\prime } = \frac {\sin \left (x \right ) \sin \left (y\right )}{\cos \left (x \right ) \cos \left (y\right )}
\]
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| \[
{} x \sec \left (y\right )^{2} y^{\prime }+1+\tan \left (y\right ) = 0
\]
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| \[
{} {\mathrm e}^{y} \left (x y^{\prime }+1\right ) = 5
\]
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| \[
{} {\mathrm e}^{x} \left (y^{\prime }+y\right ) = 3
\]
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| \[
{} \frac {y}{x}+\ln \left (x \right ) y^{\prime } = 2
\]
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| \[
{} y^{\prime } = \frac {x -y}{x +y}
\]
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| \[
{} y^{\prime } = 1+\frac {y}{x}
\]
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| \[
{} y^{\prime } = \frac {x^{2}+y^{2}}{x y}
\]
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| \[
{} y^{\prime } = \frac {y}{x}-\frac {x}{y}
\]
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| \[
{} y^{\prime } = \frac {x -y+1}{x +y+1}
\]
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| \[
{} y^{\prime } = \frac {x -y+2}{1+x}
\]
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| \[
{} y^{\prime } = \frac {x +y+2}{1+x}
\]
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| \[
{} y^{\prime }+3 y = 5
\]
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| \[
{} y^{\prime }+2 x y = x
\]
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| \[
{} y^{\prime }-2 x y = 3 x
\]
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| \[
{} y^{\prime }+7 y = {\mathrm e}^{5 x}
\]
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| \[
{} y^{\prime }-6 y = {\mathrm e}^{6 t}
\]
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| \[
{} y^{\prime }-6 y = {\mathrm e}^{6 t}
\]
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| \[
{} z^{\prime }-z \sin \left (x \right ) = {\mathrm e}^{-\cos \left (x \right )}
\]
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| \[
{} z^{\prime }-z \sin \left (x \right ) = {\mathrm e}^{-\cos \left (x \right )}
\]
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| \[
{} y^{\prime }-\frac {3 y}{x} = 5 x
\]
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|