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# |
ODE |
CAS classification |
Solved? |
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\[
{}y^{\prime } = y \left (-2+y\right ) \left (-1+y\right )
\] |
[_quadrature] |
✓ |
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\[
{}y^{\prime }+\frac {\left (y+1\right ) \left (y-1\right ) \left (y-2\right )}{x +1} = 0
\] |
[_separable] |
✓ |
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\[
{}y^{\prime } = -2 x \left (y^{3}-3 y+2\right )
\] |
[_separable] |
✓ |
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\[
{}y^{\prime }+x^{2} \left (y+1\right ) \left (y-2\right )^{2} = 0
\] |
[_separable] |
✓ |
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\[
{}x^{2}+3 x y^{\prime } = y^{3}+2 y
\] |
[_rational, _Abel] |
✓ |
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\[
{}y^{\prime } = \left (a +b x y\right ) y^{2}
\] |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
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\[
{}-a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
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\[
{}a x y^{3}+b y^{2}+y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
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\[
{}y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1} = 0
\] |
[_Abel] |
✓ |
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\[
{}y^{\prime }+\left (x +y\right ) x = x^{3} \left (x +y\right )^{3}-1
\] |
[_Abel] |
✓ |
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\[
{}y^{\prime } = y \left (2-y\right ) \left (4-y\right )
\] |
[_quadrature] |
✓ |
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\[
{}-a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
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\[
{}a x y^{3}+b y^{2}+y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
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\[
{}y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1} = 0
\] |
[_Abel] |
✓ |
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\[
{}x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n} = 0
\] |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
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\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-2 b x}+y^{3} {\mathrm e}^{-3 b x}\right ) {\mathrm e}^{b x}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
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\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-\frac {4 x}{3}}+y^{3} {\mathrm e}^{-2 x}\right ) {\mathrm e}^{\frac {2 x}{3}}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
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\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-2 x}+y^{3} {\mathrm e}^{-3 x}\right ) {\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
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\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{2 x^{2}}+y^{3} {\mathrm e}^{3 x^{2}}\right ) {\mathrm e}^{-x^{2}} x
\] |
[_Abel] |
✓ |
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\[
{}y^{\prime } = \frac {\left (-256 a \,x^{2}+512+512 y^{2}+128 y a \,x^{4}+8 a^{2} x^{8}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
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\[
{}y^{\prime } = -\frac {\left (-108 x^{{3}/{2}}-216-216 y^{2}+72 x^{3} y-6 x^{6}-216 y^{3}+108 x^{3} y^{2}-18 y x^{6}+x^{9}\right ) \sqrt {x}}{216}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
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\[
{}y^{\prime } = \frac {32 x^{5}+64 x^{6}+64 y^{2} x^{6}+32 x^{4} y+4 x^{2}+64 x^{6} y^{3}+48 x^{4} y^{2}+12 x^{2} y+1}{64 x^{8}}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
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\[
{}y^{\prime } = -\frac {\left (-8 \,{\mathrm e}^{-x^{2}}+8 x^{2} {\mathrm e}^{-x^{2}}-8-8 y^{2}+8 x^{2} {\mathrm e}^{-x^{2}} y-2 x^{4} {\mathrm e}^{-2 x^{2}}-8 y^{3}+12 x^{2} {\mathrm e}^{-x^{2}} y^{2}-6 y x^{4} {\mathrm e}^{-2 x^{2}}+x^{6} {\mathrm e}^{-3 x^{2}}\right ) x}{8}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
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\[
{}y^{\prime } = \frac {-x^{2}+x +1+y^{2}+5 x^{2} y-2 x y+4 x^{4}-3 x^{3}+y^{3}+3 y^{2} x^{2}-3 x y^{2}+3 x^{4} y-6 x^{3} y+x^{6}-3 x^{5}}{x}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
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\[
{}y^{\prime } = \frac {150 x^{3}+125 \sqrt {x}+125+125 y^{2}-100 x^{3} y-500 y \sqrt {x}+20 x^{6}+200 x^{{7}/{2}}+500 x +125 y^{3}-150 x^{3} y^{2}-750 y^{2} \sqrt {x}+60 y x^{6}+600 y x^{{7}/{2}}+1500 x y-8 x^{9}-120 x^{{13}/{2}}-600 x^{4}-1000 x^{{3}/{2}}}{125 x}
\] |
[_rational, _Abel] |
✓ |
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\[
{}y^{\prime } = \frac {-4 \cos \left (x \right ) x +4 \sin \left (x \right ) x^{2}+4 x +4+4 y^{2}+8 y \cos \left (x \right ) x -8 x y+2 x^{2} \cos \left (2 x \right )+6 x^{2}-8 x^{2} \cos \left (x \right )+4 y^{3}+12 y^{2} \cos \left (x \right ) x -12 x y^{2}+6 y x^{2} \cos \left (2 x \right )+18 x^{2} y-24 y \cos \left (x \right ) x^{2}+x^{3} \cos \left (3 x \right )+15 x^{3} \cos \left (x \right )-6 x^{3} \cos \left (2 x \right )-10 x^{3}}{4 x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
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\[
{}y^{\prime } = -\frac {x \left (-513-756 x^{3}-432 x -864 x^{4}-378 y-1134 x^{2}-576 x^{5}-216 y^{3}-540 y^{2}-972 x^{4} y^{2}-216 x^{4} y-1296 y^{2} x^{2}+720 x^{3} y-456 x^{6}-594 x^{2} y-144 x^{7}-96 x^{8}+64 x^{9}-216 x^{6} y^{3}-288 y x^{6}-216 y^{2} x^{6}+432 x^{3} y^{2}-288 y x^{8}-648 x^{4} y^{3}+288 y x^{7}+864 y^{2} x^{5}+432 y^{2} x^{7}+1008 x^{5} y-648 y^{3} x^{2}\right )}{216 \left (x^{2}+1\right )^{4}}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
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\[
{}y^{\prime } = y \left (y^{2}+y \,{\mathrm e}^{b x}+{\mathrm e}^{2 b x}\right ) {\mathrm e}^{-2 b x}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
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\[
{}y^{\prime } = y^{3}-3 y^{2} x^{2}+3 x^{4} y-x^{6}+2 x
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
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\[
{}y^{\prime } = y^{3}+y^{2} x^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27}-\frac {2 x}{3}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
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\[
{}y^{\prime } = y \left (y^{2}+{\mathrm e}^{-x^{2}} y+{\mathrm e}^{-2 x^{2}}\right ) {\mathrm e}^{2 x^{2}} x
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Abel] |
✓ |
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\[
{}y^{\prime } = \frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x}{x}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Abel] |
✓ |
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\[
{}y^{\prime } = \frac {x^{3} y^{3}+6 y^{2} x^{2}+12 x y+8+2 x}{x^{3}}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
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\[
{}y^{\prime } = \frac {y^{3} a^{3} x^{3}+3 y^{2} a^{2} x^{2}+3 y a x +1+a^{2} x}{x^{3} a^{3}}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
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\[
{}y^{\prime } = \frac {\left (1+x y\right ) \left (y^{2} x^{2}+x^{2} y+2 x y+1+x +x^{2}\right )}{x^{5}}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
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\[
{}y^{\prime } = \frac {y^{3}-3 x y^{2} \ln \left (x \right )+3 x^{2} \ln \left (x \right )^{2} y-x^{3} \ln \left (x \right )^{3}+x^{2}+x y}{x^{2}}
\] |
[_Abel] |
✓ |
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\[
{}x^{\prime } = -x \left (-x+1\right ) \left (2-x\right )
\] |
[_quadrature] |
✓ |
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\[
{}y^{\prime }-y^{3} = 8
\] |
[_quadrature] |
✓ |
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\[
{}y^{\prime } = y^{3}+1
\] |
[_quadrature] |
✓ |
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\[
{}y^{\prime } = y^{3}-1
\] |
[_quadrature] |
✓ |
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