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ODE |
Mathematica |
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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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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )+3 z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )-4 z \left (t \right ), z^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )+z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )-4 t +1, y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )+3 t +4]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )-t +3, y^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right )+t -2]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right )-t +3, y^{\prime }\left (t \right ) = -x \left (t \right )-5 y \left (t \right )+t +1]
\] |
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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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\[
{}[x^{\prime }\left (t \right ) = t y \left (t \right )+1, y^{\prime }\left (t \right ) = -t x \left (t \right )+y \left (t \right )]
\] |
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\[
{}y^{\prime } = y^{2}-x
\] |
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\[
{}y^{\prime } = y^{2}-x
\] |
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\[
{}y^{\prime }-2 y = x^{2}
\] |
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\[
{}y^{\prime }-2 y = x^{2}
\] |
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\[
{}y^{\prime } = y+x \,{\mathrm e}^{y}
\] |
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\[
{}y^{\prime } = y+x \,{\mathrm e}^{y}
\] |
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\[
{}y^{\prime \prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+y = 0
\] |
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\[
{}y^{\prime \prime }-y = 0
\] |
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\[
{}y^{\prime \prime }-y = 0
\] |
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\[
{}y^{\prime \prime }-y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }-y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }-x y = 0
\] |
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\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
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\[
{}y^{\prime \prime }-2 x y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }-x y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }+x^{2} y^{\prime }+x y = 0
\] |
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\[
{}y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\] |
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\[
{}\left (x -1\right ) y^{\prime \prime }+y^{\prime } = 0
\] |
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\[
{}\left (x +2\right ) y^{\prime \prime }+x y^{\prime }-y = 0
\] |
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\[
{}y^{\prime \prime }-\left (1+x \right ) y^{\prime }-y = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0
\] |
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\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0
\] |
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\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }-y = 0
\] |
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\[
{}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
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\[
{}\left (1+x \right ) y^{\prime \prime }-\left (2-x \right ) y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }-2 x y^{\prime }+8 y = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y = 0
\] |
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\[
{}\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y = 0
\] |
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\[
{}\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y = 0
\] |
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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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\[
{}x y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }+5 x y^{\prime }+\sqrt {x}\, y = 0
\] |
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\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+y \cos \left (x \right ) = 0
\] |
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\[
{}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0
\] |
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\[
{}x \left (x +3\right )^{2} y^{\prime \prime }-y = 0
\] |
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\[
{}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}} = 0
\] |
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\[
{}\left (x^{3}+4 x \right ) y^{\prime \prime }-2 x y^{\prime }+6 y = 0
\] |
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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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\[
{}\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (x -2\right ) y = 0
\] |
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\[
{}x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y = 0
\] |
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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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\[
{}\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (1+x \right ) y = 0
\] |
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\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+5 \left (1+x \right ) y^{\prime }+\left (x^{2}-x \right ) y = 0
\] |
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\[
{}x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0
\] |
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\[
{}x y^{\prime \prime }+y^{\prime }+10 y = 0
\] |
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\[
{}2 x y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
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\[
{}2 x y^{\prime \prime }+5 y^{\prime }+x y = 0
\] |
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\[
{}4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y = 0
\] |
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\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
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\[
{}3 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y = 0
\] |
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\[
{}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{9}\right ) y = 0
\] |
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\[
{}9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y = 0
\] |
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\[
{}2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0
\] |
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\[
{}x y^{\prime \prime }+2 y^{\prime }-x y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
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\[
{}x y^{\prime \prime }-x y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y = 0
\] |
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\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0
\] |
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\[
{}x y^{\prime \prime }+y^{\prime }+y = 0
\] |
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\[
{}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0
\] |
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\[
{}x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{t}+\lambda y = 0
\] |
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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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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0
\] |
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\[
{}16 x^{2} y^{\prime \prime }+16 x y^{\prime }+\left (16 x^{2}-1\right ) y = 0
\] |
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\[
{}x y^{\prime \prime }+y^{\prime }+x y = 0
\] |
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\[
{}y^{\prime }+x y^{\prime \prime }+\left (x -\frac {4}{x}\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0
\] |
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\[
{}x y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
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\[
{}x y^{\prime \prime }+3 y^{\prime }+x y = 0
\] |
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\[
{}x y^{\prime \prime }-y^{\prime }+x y = 0
\] |
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\[
{}x y^{\prime \prime }-5 y^{\prime }+x y = 0
\] |
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