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# |
ODE |
Mathematica |
Maple |
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\[
{}[x^{\prime }\left (t \right ) = -3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right )+3 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right )-t^{2}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = t x \left (t \right )-{\mathrm e}^{t} y \left (t \right )+\cos \left (t \right ), y^{\prime }\left (t \right ) = {\mathrm e}^{-t} x \left (t \right )+t^{2} y \left (t \right )-\sin \left (t \right )]
\] |
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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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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = 5 y \left (t \right )-7 z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )+z \left (t \right )+t, y^{\prime }\left (t \right ) = x \left (t \right )-3 z \left (t \right )+t^{2}, z^{\prime }\left (t \right ) = 6 y \left (t \right )-7 z \left (t \right )+t^{3}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = t x \left (t \right )-y \left (t \right )+{\mathrm e}^{t} z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+t^{2} y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = {\mathrm e}^{-t} x \left (t \right )+3 t y \left (t \right )+t^{3} z \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )+x_{3} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = x_{3} \left (t \right )+x_{4} \left (t \right )+t, x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{4} \left (t \right )+t^{2}, x_{4}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+t^{3}]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-7 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+3 x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )-11 x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+9 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -6 x_{1} \left (t \right )-6 x_{2} \left (t \right )+x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-12 x_{2} \left (t \right )-x_{3} \left (t \right )-6 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -4 x_{2} \left (t \right )-x_{4} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-7 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )+5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -6 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-5 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-9 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -50 x_{1} \left (t \right )+20 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 100 x_{1} \left (t \right )-60 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+7 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+4 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )+5 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-6 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-2 x_{2} \left (t \right )-4 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+4 x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -6 x_{1} \left (t \right )-6 x_{2} \left (t \right )-5 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+5 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -9 x_{1} \left (t \right )+4 x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 4 x_{3} \left (t \right )+4 x_{4} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+9 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right )-10 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{3} \left (t \right )+8 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{4} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -21 x_{1} \left (t \right )-5 x_{2} \left (t \right )-27 x_{3} \left (t \right )-9 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -21 x_{3} \left (t \right )-2 x_{4} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+7 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+4 x_{2} \left (t \right )+10 x_{3} \left (t \right )+x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+10 x_{2} \left (t \right )+4 x_{3} \left (t \right )+x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+4 x_{4} \left (t \right )]
\] |
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\[
{}y^{\prime } = 2 x +1
\] |
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\[
{}y^{\prime } = \left (x -2\right )^{2}
\] |
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\[
{}y^{\prime } = \sqrt {x}
\] |
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\[
{}y^{\prime } = \frac {1}{x^{2}}
\] |
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\[
{}y^{\prime } = \frac {1}{\sqrt {x +2}}
\] |
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\[
{}y^{\prime } = x \sqrt {x^{2}+9}
\] |
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\[
{}y^{\prime } = \frac {10}{x^{2}+1}
\] |
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\[
{}y^{\prime } = \cos \left (2 x \right )
\] |
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\[
{}y^{\prime } = \frac {1}{\sqrt {-x^{2}+1}}
\] |
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\[
{}y^{\prime } = x \,{\mathrm e}^{-x}
\] |
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\[
{}y^{\prime } = -\sin \left (x \right )-y
\] |
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\[
{}y^{\prime } = x +y
\] |
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\[
{}y^{\prime } = -\sin \left (x \right )+y
\] |
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\[
{}y^{\prime } = x -y
\] |
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\[
{}y^{\prime } = y-x +1
\] |
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\[
{}y^{\prime } = x -y+1
\] |
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\[
{}y^{\prime } = x^{2}-y
\] |
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\[
{}y^{\prime } = -2+x^{2}-y
\] |
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\[
{}y^{\prime } = 2 x^{2} y^{2}
\] |
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\[
{}y^{\prime } = x \ln \left (y\right )
\] |
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\[
{}y^{\prime } = y^{{1}/{3}}
\] |
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\[
{}y^{\prime } = y^{{1}/{3}}
\] |
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\[
{}y y^{\prime } = x -1
\] |
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\[
{}y y^{\prime } = x -1
\] |
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\[
{}y^{\prime } = \ln \left (1+y^{2}\right )
\] |
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\[
{}y^{\prime } = x^{2}-y^{2}
\] |
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\[
{}2 x y+y^{\prime } = 0
\] |
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\[
{}2 x y^{2}+y^{\prime } = 0
\] |
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\[
{}y^{\prime } = y \sin \left (x \right )
\] |
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\[
{}\left (1+x \right ) y^{\prime } = 4 y
\] |
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\[
{}2 y^{\prime } \sqrt {x} = \sqrt {1-y^{2}}
\] |
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\[
{}y^{\prime } = 3 \sqrt {x y}
\] |
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\[
{}y^{\prime } = 4 \left (x y\right )^{{1}/{3}}
\] |
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\[
{}y^{\prime } = 2 x \sec \left (y\right )
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime } = 2 y
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime } = \left (1+y\right )^{2}
\] |
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\[
{}y^{\prime } = x y^{3}
\] |
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\[
{}y y^{\prime } = x \left (1+y^{2}\right )
\] |
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\[
{}y^{\prime } = \frac {1+\sqrt {x}}{1+\sqrt {y}}
\] |
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\[
{}y^{\prime } = \frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )}
\] |
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\[
{}\left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime } = x
\] |
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\[
{}y^{\prime } = 1+x +y+x y
\] |
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\[
{}x^{2} y^{\prime } = 1-x^{2}+y^{2}-x^{2} y^{2}
\] |
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\[
{}y^{\prime } = y \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime } = 3 x^{2} \left (1+y^{2}\right )
\] |
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\[
{}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}}
\] |
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\[
{}y^{\prime } = 4 x^{3} y-y
\] |
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\[
{}1+y^{\prime } = 2 y
\] |
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\[
{}\tan \left (x \right ) y^{\prime } = y
\] |
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\[
{}x y^{\prime }-y = 2 x^{2} y
\] |
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