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# |
ODE |
CAS classification |
Solved? |
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\[
{}1+x y \left (1+x y^{2}\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
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\[
{}y^{\prime } = \frac {1}{x y+x^{3} y^{3}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
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\[
{}x \left (x^{3}-3 x^{3} y+4 y^{2}\right ) y^{\prime } = 6 y^{3}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
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\[
{}\left (x +2 y+2 x^{2} y^{3}+x y^{4}\right ) y^{\prime }+\left (1+y^{4}\right ) y = 0
\] |
[_rational] |
✓ |
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\[
{}\left (-x^{2}+1\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+4 x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
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\[
{}x y {y^{\prime }}^{2}+\left (a +x^{2}-y^{2}\right ) y^{\prime }-x y = 0
\] |
[_rational] |
✓ |
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\[
{}\left (x^{2} y^{3}+x y\right ) y^{\prime }-1 = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
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\[
{}\left (x +2 y+2 x^{2} y^{3}+x y^{4}\right ) y^{\prime }+y^{5}+y = 0
\] |
[_rational] |
✓ |
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\[
{}a x y {y^{\prime }}^{2}-\left (y^{2} a +b \,x^{2}+c \right ) y^{\prime }+b x y = 0
\] |
[_rational] |
✓ |
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\[
{}a \left ({y^{\prime }}^{3}+1\right )^{{1}/{3}}+b x y^{\prime }-y = 0
\] |
[_dAlembert] |
✓ |
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\[
{}y^{\prime } = \frac {1}{x \left (x y^{2}+1+x \right ) y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
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\[
{}y^{\prime } = \frac {2 y^{6}}{y^{3}+2+16 x y^{2}+32 x^{2} y^{4}}
\] |
[_rational] |
✓ |
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\[
{}y^{\prime } = \frac {y \left (x -y\right ) \left (1+y\right )}{x \left (x y+x -y\right )}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
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\[
{}y^{\prime } = \frac {y \left (x +y\right ) \left (1+y\right )}{x \left (x y+x +y\right )}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
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\[
{}y^{\prime } = -\left (-\frac {\ln \left (y\right )}{x}+\frac {\cos \left (x \right ) \ln \left (y\right )}{\sin \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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\[
{}y^{\prime } = \frac {2 y^{8}}{y^{5}+2 y^{6}+2 y^{2}+16 x y^{4}+32 y^{6} x^{2}+2+24 x y^{2}+96 x^{2} y^{4}+128 x^{3} y^{6}}
\] |
[_rational] |
✓ |
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\[
{}y^{\prime } = -\left (-\frac {\ln \left (y\right )}{x}+\frac {\ln \left (y\right )}{x \ln \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
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\[
{}y^{\prime } = -\frac {\left (-\frac {\ln \left (y\right )^{2}}{2 x}-\textit {\_F1} \left (x \right )\right ) y}{\ln \left (y\right )}
\] |
[NONE] |
✓ |
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\[
{}y^{\prime } = -\frac {216 y}{-216 y^{4}-252 y^{3}-396 y^{2}-216 y+36 x^{2}-72 x y+60 y^{5}-36 x y^{3}-72 x y^{2}-24 x y^{4}+4 y^{8}+12 y^{7}+33 y^{6}}
\] |
[_rational] |
✓ |
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\[
{}y^{\prime } = -\frac {1296 y}{216+216 x^{3}-324 x^{2} y^{3}-432 x y+216 x y^{2}-1944 y^{4}-648 y^{2} x^{2}-126 y^{10}-315 y^{9}-8 y^{12}-36 y^{11}-846 y^{7}+1152 x y^{4}-1728 y^{3}-612 y^{5}-1296 y+216 x^{2}-2376 y^{2}-570 y^{8}-216 x^{2} y^{4}-648 x^{2} y+1080 x y^{3}+72 y^{8} x +216 y^{7} x +594 x y^{6}+1080 y^{5} x -882 y^{6}}
\] |
[_rational] |
✓ |
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\[
{}\left (x^{2} y^{3}+x y\right ) y^{\prime } = 1
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
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\[
{}\left (x^{2} y^{3}+x y\right ) y^{\prime } = 1
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
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\[
{}\left (x^{2} y^{3}+x y\right ) y^{\prime } = 1
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
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