Number of problems in this table is 31
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# |
ODE |
CAS classification |
Solved? |
Verified? |
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\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right )^{\frac {1}{3}} \] |
[_quadrature] |
✓ |
✓ |
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\[ {}\frac {d}{d x}y \left (x \right ) = {| y \left (x \right )|}+1 \] |
[_quadrature] |
✓ |
✓ |
|
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\[ {}\frac {d}{d x}y \left (x \right ) = 3 x \left (y \left (x \right )-1\right )^{\frac {1}{3}} \] |
[_separable] |
✓ |
✓ |
|
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\[ {}\frac {d}{d x}y \left (x \right ) = \frac {2 \sqrt {y \left (x \right )-1}}{3} \] |
[_quadrature] |
✓ |
✓ |
|
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\[ {}x +y \left (x \right )+\left (x -y \left (x \right )\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
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\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right )^{\frac {1}{3}} \] |
[_quadrature] |
✓ |
✓ |
|
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\[ {}\frac {d}{d x}y \left (x \right ) = 3 y \left (x \right )^{\frac {2}{3}} \] |
[_quadrature] |
✓ |
✓ |
|
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\[ {}\frac {d}{d x}y \left (x \right ) = 2 \sqrt {y \left (x \right )} \] |
[_quadrature] |
✓ |
✓ |
|
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\[ {}\frac {d}{d x}y \left (x \right ) = 2 \sqrt {y \left (x \right )} \] |
[_quadrature] |
✓ |
✓ |
|
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\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right )^{\frac {1}{3}} \] |
[_quadrature] |
✓ |
✓ |
|
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\[ {}\frac {d}{d x}y \left (x \right ) = y \left (x \right )^{\frac {1}{3}} \] |
[_quadrature] |
✓ |
✓ |
|
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\[ {}\frac {d}{d x}y \left (x \right ) = -x \sqrt {1-y \left (x \right )^{2}} \] |
[_separable] |
✓ |
✓ |
|
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\[ {}\frac {d}{d x}y \left (x \right ) = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y \left (x \right )}}{2} \] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
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\[ {}\frac {d}{d x}y \left (x \right ) = \frac {\sqrt {y \left (x \right )}}{x} \] |
[_separable] |
✓ |
✓ |
|
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\[ {}\frac {d}{d x}y \left (x \right ) = 3 x y \left (x \right )^{\frac {1}{3}} \] |
[_separable] |
✓ |
✓ |
|
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\[ {}\frac {d}{d x}y \left (x \right ) = \sqrt {\left (y \left (x \right )+2\right ) \left (y \left (x \right )-1\right )} \] |
[_quadrature] |
✓ |
✓ |
|
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\[ {}\frac {d}{d x}y \left (x \right ) = \frac {x y \left (x \right )}{x^{2}+y \left (x \right )^{2}} \] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
|
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\[ {}\frac {d}{d x}y \left (x \right ) = x \sqrt {1-y \left (x \right )^{2}} \] |
[_separable] |
✓ |
✓ |
|
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\[ {}\frac {d}{d x}y \left (x \right ) = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y \left (x \right )}}{2} \] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
|
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\[ {}\frac {d}{d x}y \left (x \right ) = 2 \sqrt {y \left (x \right )} \] |
[_quadrature] |
✓ |
✓ |
|
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\[ {}y^{\prime }\left (t \right ) = y \left (t \right )^{\frac {1}{5}} \] |
[_quadrature] |
✓ |
✓ |
|
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\[ {}\frac {y^{\prime }\left (t \right )}{t} = \sqrt {y \left (t \right )} \] |
[_separable] |
✓ |
✓ |
|
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\[ {}y^{\prime }\left (t \right ) = 6 y \left (t \right )^{\frac {2}{3}} \] |
[_quadrature] |
✓ |
✓ |
|
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\[ {}y^{\prime }\left (t \right ) = \sqrt {y \left (t \right )^{2}-1} \] |
[_quadrature] |
✓ |
✓ |
|
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\[ {}y^{\prime }\left (t \right ) = \sqrt {y \left (t \right )^{2}-1} \] |
[_quadrature] |
✓ |
✓ |
|
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\[ {}y^{\prime }\left (t \right ) = \sqrt {25-y \left (t \right )^{2}} \] |
[_quadrature] |
✓ |
✓ |
|
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\[ {}y^{\prime }\left (t \right ) = \sqrt {25-y \left (t \right )^{2}} \] |
[_quadrature] |
✓ |
✓ |
|
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\[ {}-2 x -y \left (x \right ) \cos \left (x y \left (x \right )\right )+\left (2 y \left (x \right )-x \cos \left (x y \left (x \right )\right )\right ) \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_exact] |
✓ |
✓ |
|
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\[ {}\frac {d}{d x}y \left (x \right ) = \sqrt {x -y \left (x \right )} \] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
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\[ {}x \sqrt {1-y \left (x \right )^{2}}+y \left (x \right ) \sqrt {-x^{2}+1}\, \left (\frac {d}{d x}y \left (x \right )\right ) = 0 \] |
[_separable] |
✓ |
✓ |
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\[ {}x^{2} \left (\frac {d}{d x}y \left (x \right )\right )+\sin \left (2 y \left (x \right )\right ) = 1 \] |
[_separable] |
✓ |
✗ |
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