|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime } = 2 x +1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.385 |
|
|
\[ {}y^{\prime } = \left (-2+x \right )^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.29 |
|
|
\[ {}y^{\prime } = \sqrt {x} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.321 |
|
|
\[ {}y^{\prime } = \frac {1}{x^{2}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.26 |
|
|
\[ {}y^{\prime } = \frac {1}{\sqrt {2+x}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.297 |
|
|
\[ {}y^{\prime } = x \sqrt {x^{2}+9} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.384 |
|
|
\[ {}y^{\prime } = \frac {10}{x^{2}+1} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.341 |
|
|
\[ {}y^{\prime } = \cos \left (2 x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.352 |
|
|
\[ {}y^{\prime } = \frac {1}{\sqrt {-x^{2}+1}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.445 |
|
|
\[ {}y^{\prime } = x \,{\mathrm e}^{-x} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.187 |
|
|
\[ {}y^{\prime } = -\sin \left (x \right )-y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.63 |
|
|
\[ {}y^{\prime } = x +y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.374 |
|
|
\[ {}y^{\prime } = -\sin \left (x \right )+y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.482 |
|
|
\[ {}y^{\prime } = x -y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.379 |
|
|
\[ {}y^{\prime } = -x +y+1 \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.482 |
|
|
\[ {}y^{\prime } = x -y+1 \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.478 |
|
|
\[ {}y^{\prime } = x^{2}-y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.381 |
|
|
\[ {}y^{\prime } = -2+x^{2}-y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.549 |
|
|
\[ {}y^{\prime } = 2 x^{2} y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.164 |
|
|
\[ {}y^{\prime } = x \ln \left (y\right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.699 |
|
|
\[ {}y^{\prime } = y^{\frac {1}{3}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.436 |
|
|
\[ {}y^{\prime } = y^{\frac {1}{3}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.234 |
|
|
\[ {}y y^{\prime } = -1+x \] |
exact, separable, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
4.47 |
|
|
\[ {}y y^{\prime } = -1+x \] |
exact, separable, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.789 |
|
|
\[ {}y^{\prime } = \ln \left (1+y^{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.426 |
|
|
\[ {}y^{\prime } = x^{2}-y^{2} \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.438 |
|
|
\[ {}2 x y+y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.871 |
|
|
\[ {}2 x y^{2}+y^{\prime } = 0 \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.578 |
|
|
\[ {}y^{\prime } = \sin \left (x \right ) y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.98 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = 4 y \] |
exact, linear, separable, homogeneousTypeD2, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.167 |
|
|
\[ {}2 \sqrt {x}\, y^{\prime } = \sqrt {1-y^{2}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.404 |
|
|
\[ {}y^{\prime } = 3 \sqrt {x y} \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
11.688 |
|
|
\[ {}y^{\prime } = 4 \left (x y\right )^{\frac {1}{3}} \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
91.221 |
|
|
\[ {}y^{\prime } = 2 x \sec \left (y\right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.791 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = 2 y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.298 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = \left (y+1\right )^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.967 |
|
|
\[ {}y^{\prime } = x y^{3} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.805 |
|
|
\[ {}y y^{\prime } = x \left (1+y^{2}\right ) \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.931 |
|
|
\[ {}y^{\prime } = \frac {1+\sqrt {x}}{1+\sqrt {y}} \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
170.809 |
|
|
\[ {}y^{\prime } = \frac {\left (-1+x \right ) y^{5}}{x^{2} \left (-y+2 y^{3}\right )} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
18.824 |
|
|
\[ {}\left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime } = x \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.432 |
|
|
\[ {}y^{\prime } = 1+x +y+x y \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.866 |
|
|
\[ {}x^{2} y^{\prime } = 1-x^{2}+y^{2}-x^{2} y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.188 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x} y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.815 |
|
|
\[ {}y^{\prime } = 3 x^{2} \left (1+y^{2}\right ) \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.2 |
|
|
\[ {}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
5.32 |
|
|
\[ {}y^{\prime } = -y+4 x^{3} y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.009 |
|
|
\[ {}1+y^{\prime } = 2 y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.476 |
|
|
\[ {}\tan \left (x \right ) y^{\prime } = y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.139 |
|
|
\[ {}-y+x y^{\prime } = 2 x^{2} y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.973 |
|
|
\[ {}y^{\prime } = 2 x y^{2}+3 x^{2} y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.709 |
|
|
\[ {}y^{\prime } = 6 \,{\mathrm e}^{2 x -y} \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.887 |
|
|
\[ {}2 \sqrt {x}\, y^{\prime } = \cos \left (y\right )^{2} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.51 |
|
|
\[ {}y+y^{\prime } = 2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.481 |
|
|
\[ {}-2 y+y^{\prime } = 3 \,{\mathrm e}^{2 x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.601 |
|
|
\[ {}3 y+y^{\prime } = 2 x \,{\mathrm e}^{-3 x} \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.821 |
|
|
\[ {}-2 x y+y^{\prime } = {\mathrm e}^{x^{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.777 |
|
|
\[ {}2 y+x y^{\prime } = 3 x \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.953 |
|
|
\[ {}y+2 x y^{\prime } = 10 \sqrt {x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.926 |
|
|
\[ {}y+2 x y^{\prime } = 10 \sqrt {x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.698 |
|
|
\[ {}y+3 x y^{\prime } = 12 x \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.562 |
|
|
\[ {}-y+x y^{\prime } = x \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.707 |
|
|
\[ {}-3 y+2 x y^{\prime } = 9 x^{3} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.832 |
|
|
\[ {}y+x y^{\prime } = 3 x y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.724 |
|
|
\[ {}3 y+x y^{\prime } = 2 x^{5} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.616 |
|
|
\[ {}y+y^{\prime } = {\mathrm e}^{x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.529 |
|
|
\[ {}-3 y+x y^{\prime } = x^{3} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.654 |
|
|
\[ {}2 x y+y^{\prime } = x \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.03 |
|
|
\[ {}y^{\prime } = \cos \left (x \right ) \left (1-y\right ) \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.056 |
|
|
\[ {}y+\left (1+x \right ) y^{\prime } = \cos \left (x \right ) \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.727 |
|
|
\[ {}x y^{\prime } = x^{3} \cos \left (x \right )+2 y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.968 |
|
|
\[ {}\cot \left (x \right ) y+y^{\prime } = \cos \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.103 |
|
|
\[ {}y^{\prime } = 1+x +y+x y \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.757 |
|
|
\[ {}x y^{\prime } = x^{4} \cos \left (x \right )+3 y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.804 |
|
|
\[ {}y^{\prime } = 3 x^{2} {\mathrm e}^{x^{2}}+2 x y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.689 |
|
|
\[ {}\left (2 x -3\right ) y+x y^{\prime } = 4 x^{4} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.961 |
|
|
\[ {}3 x y+\left (x^{2}+4\right ) y^{\prime } = x \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.406 |
|
|
\[ {}3 x^{3} y+\left (x^{2}+1\right ) y^{\prime } = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
3.8 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = x -y \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.521 |
|
|
\[ {}2 x y y^{\prime } = x^{2}+y^{2} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.878 |
|
|
\[ {}x y^{\prime } = y+2 \sqrt {x y} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.587 |
|
|
\[ {}\left (x -y\right ) y^{\prime } = x +y \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.955 |
|
|
\[ {}x \left (x +y\right ) y^{\prime } = y \left (x -y\right ) \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.985 |
|
|
\[ {}\left (2 y+x \right ) y^{\prime } = y \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.862 |
|
|
\[ {}x y^{2} y^{\prime } = x^{3}+y^{3} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.965 |
|
|
\[ {}x^{2} y^{\prime } = {\mathrm e}^{\frac {y}{x}} x^{2}+x y \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.047 |
|
|
\[ {}x^{2} y^{\prime } = x y+y^{2} \] |
riccati, bernoulli, exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.517 |
|
|
\[ {}x y y^{\prime } = x^{2}+3 y^{2} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.107 |
|
|
\[ {}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.424 |
|
|
\[ {}x y y^{\prime } = y^{2}+x \sqrt {4 x^{2}+y^{2}} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.627 |
|
|
\[ {}x y^{\prime } = y+\sqrt {x^{2}+y^{2}} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.341 |
|
|
\[ {}x +y y^{\prime } = \sqrt {x^{2}+y^{2}} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.68 |
|
|
\[ {}y \left (3 x +y\right )+x \left (x +y\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.957 |
|
|
\[ {}y^{\prime } = \sqrt {1+x +y} \] |
homogeneousTypeC, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
2.654 |
|
|
\[ {}y^{\prime } = \left (4 x +y\right )^{2} \] |
riccati, homogeneousTypeC, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.915 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.12 |
|
|
\[ {}2 x y+x^{2} y^{\prime } = 5 y^{3} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.892 |
|
|
\[ {}2 x y^{3}+y^{2} y^{\prime } = 6 x \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.352 |
|
|
\[ {}y^{\prime } = y+y^{3} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.649 |
|
|
\[ {}2 x y+x^{2} y^{\prime } = 5 y^{4} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.335 |
|
|
|
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