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ODE |
Mathematica |
Maple |
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\[
{}4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y = x^{{5}/{2}} {\mathrm e}^{x}
\] |
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\[
{}\left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y = \left (3 x -1\right )^{2} {\mathrm e}^{2 x}
\] |
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\[
{}\left (x -1\right )^{2} y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+2 y = \left (x -1\right )^{2}
\] |
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\[
{}\left (x -1\right )^{2} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+\left (1+x \right ) y = \left (x -1\right )^{3} {\mathrm e}^{x}
\] |
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\[
{}\left (x -1\right )^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 x
\] |
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\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = -2 x^{2}
\] |
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\[
{}\left (1+x \right ) \left (2 x +3\right ) y^{\prime \prime }+2 \left (x +2\right ) y^{\prime }-2 y = \left (2 x +3\right )^{2}
\] |
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\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y = 0
\] |
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\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y = 0
\] |
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\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y = 0
\] |
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\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y = 0
\] |
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\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y = 0
\] |
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\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 2 x
\] |
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\[
{}4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 x y^{\prime }+2 y = 30 x^{2}
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}
\] |
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\[
{}16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 x y^{\prime }+9 y = 96 x^{{5}/{2}}
\] |
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\[
{}x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 x y^{\prime }+24 y = x^{4}
\] |
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\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = 12 x^{2}
\] |
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\[
{}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 4 x
\] |
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\[
{}x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y = x^{3}
\] |
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\[
{}x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+16 x y^{\prime }-16 y = 9 x^{4}
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \left (1+x \right )
\] |
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\[
{}x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 9 x^{2}
\] |
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\[
{}4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-x y^{\prime }+y = 6 x
\] |
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\[
{}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 x y^{\prime }+6 y = 40 x^{3}
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = F \left (x \right )
\] |
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\[
{}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = F \left (x \right )
\] |
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\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\] |
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\[
{}y^{\prime \prime }+t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-t y^{\prime }-2 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0
\] |
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\[
{}y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0
\] |
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\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\] |
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\[
{}\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\] |
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\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0
\] |
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\[
{}\left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {t^{2} y}{4} = f \cos \left (t \right )
\] |
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\[
{}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1
\] |
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\[
{}t^{2} y^{\prime \prime }-5 t y^{\prime }+9 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0
\] |
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\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\] |
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\[
{}\left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\] |
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\[
{}\left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+2 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0
\] |
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\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\] |
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\[
{}y^{\prime \prime }+t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+5 t y^{\prime }-2 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0
\] |
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\[
{}y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0
\] |
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\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\] |
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\[
{}\left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\] |
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\[
{}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0
\] |
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\[
{}\left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0
\] |
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\[
{}t y^{\prime \prime }-\left (1+3 t \right ) y^{\prime }+3 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-2 y = t^{2}
\] |
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\[
{}y^{\prime \prime }+p \left (t \right ) y^{\prime }+q \left (t \right ) y = t +1
\] |
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\[
{}y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1} = t^{2}+1
\] |
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\[
{}t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0
\] |
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\[
{}2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\] |
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\[
{}\left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\] |
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\[
{}\left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+2 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-t y^{\prime }-2 y = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0
\] |
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\[
{}z^{\prime \prime }+z^{3} = 0
\] |
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\[
{}z^{\prime \prime }+z+z^{5} = 0
\] |
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\[
{}z^{\prime \prime }+{\mathrm e}^{z^{2}} = 1
\] |
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\[
{}z^{\prime \prime }+\frac {z}{1+z^{2}} = 0
\] |
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\[
{}z^{\prime \prime }+z-2 z^{3} = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+16 y = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }-16 x y^{\prime }+25 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+10 y = 0
\] |
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\[
{}2 x^{2} y^{\prime \prime }-3 x y^{\prime }-18 y = \ln \left (x \right )
\] |
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\[
{}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = \ln \left (x^{2}\right )
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{3}
\] |
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\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 1-x
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {1}{x}
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 4 x +\sin \left (\ln \left (x \right )\right )
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = \ln \left (x \right ) x^{2}
\] |
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