|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime } = \sqrt {x^{2}+1} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.291 |
|
|
\[ {}y^{\prime }+4 y = 8 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.28 |
|
|
\[ {}y^{\prime }+x y = 4 x \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.996 |
|
|
\[ {}y^{\prime }+4 y = x^{2} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.684 |
|
|
\[ {}y^{\prime } = x y-3 x -2 y+6 \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.914 |
|
|
\[ {}y^{\prime } = \sin \left (x +y\right ) \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.269 |
|
|
\[ {}y y^{\prime } = {\mathrm e}^{x -3 y^{2}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.176 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.408 |
|
|
\[ {}y^{\prime } = y^{2}+9 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.246 |
|
|
\[ {}x y y^{\prime } = y^{2}+9 \] |
exact, bernoulli, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.068 |
|
|
\[ {}y^{\prime } = \frac {1+y^{2}}{x^{2}+1} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.79 |
|
|
\[ {}\cos \left (y\right ) y^{\prime } = \sin \left (x \right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.252 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{2 x -3 y} \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.785 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.223 |
|
|
\[ {}y^{\prime } = 2 x -1+2 x y-y \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.231 |
|
|
\[ {}y y^{\prime } = x y^{2}+x \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.479 |
|
|
\[ {}y y^{\prime } = 3 \sqrt {x y^{2}+9 x} \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
2.664 |
|
|
\[ {}y^{\prime } = x y-4 x \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.863 |
|
|
\[ {}y^{\prime }-4 y = 2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.276 |
|
|
\[ {}y y^{\prime } = x y^{2}-9 x \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.435 |
|
|
\[ {}y^{\prime } = \sin \left (y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.402 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x +y^{2}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.653 |
|
|
\[ {}y^{\prime } = 200 y-2 y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.574 |
|
|
\[ {}y^{\prime } = x y-4 x \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.678 |
|
|
\[ {}y^{\prime } = x y-3 x -2 y+6 \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.895 |
|
|
\[ {}y^{\prime } = 3 y^{2}-y^{2} \sin \left (x \right ) \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.82 |
|
|
\[ {}y^{\prime } = \tan \left (y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.195 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.754 |
|
|
\[ {}y^{\prime } = \frac {6 x^{2}+4}{3 y^{2}-4 y} \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
163.516 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.79 |
|
|
\[ {}\left (y^{2}-1\right ) y^{\prime } = 4 x y^{2} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.783 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{-y} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.171 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{-y}+1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.607 |
|
|
\[ {}y^{\prime } = 3 x y^{3} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.864 |
|
|
\[ {}y^{\prime } = \frac {2+\sqrt {x}}{2+\sqrt {y}} \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
99.218 |
|
|
\[ {}y^{\prime }-3 x^{2} y^{2} = -3 x^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.275 |
|
|
\[ {}y^{\prime }-3 x^{2} y^{2} = 3 x^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.945 |
|
|
\[ {}y^{\prime } = 200 y-2 y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.2 |
|
|
\[ {}y^{\prime }-2 y = -10 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.477 |
|
|
\[ {}y y^{\prime } = \sin \left (x \right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.444 |
|
|
\[ {}y^{\prime } = 2 x -1+2 x y-y \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.051 |
|
|
\[ {}x y^{\prime } = y^{2}-y \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.388 |
|
|
\[ {}x y^{\prime } = y^{2}-y \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.352 |
|
|
\[ {}y^{\prime } = \frac {y^{2}-1}{x y} \] |
exact, bernoulli, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
7.687 |
|
|
\[ {}\left (y^{2}-1\right ) y^{\prime } = 4 x y \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
4.379 |
|
|
\[ {}x^{2} y^{\prime }+3 x^{2} y = \sin \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.36 |
|
|
\[ {}y^{2} y^{\prime }+3 x^{2} y = \sin \left (x \right ) \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
1.335 |
|
|
\[ {}y^{\prime }-x y^{2} = \sqrt {x} \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.527 |
|
|
\[ {}y^{\prime } = 1+\left (x y+3 y\right )^{2} \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.67 |
|
|
\[ {}y^{\prime } = 1+x y+3 y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.843 |
|
|
\[ {}y^{\prime } = 4 y+8 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.277 |
|
|
\[ {}y^{\prime }-{\mathrm e}^{2 x} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.123 |
|
|
\[ {}y^{\prime } = y \sin \left (x \right ) \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.004 |
|
|
\[ {}y^{\prime }+4 y = y^{3} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.278 |
|
|
\[ {}x y^{\prime }+\cos \left (x^{2}\right ) = 827 y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
36.53 |
|
|
\[ {}y^{\prime }+2 y = 6 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.285 |
|
|
\[ {}y^{\prime }+2 y = 20 \,{\mathrm e}^{3 x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.733 |
|
|
\[ {}y^{\prime } = 4 y+16 x \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.691 |
|
|
\[ {}y^{\prime }-2 x y = x \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.043 |
|
|
\[ {}x y^{\prime }+3 y-10 x^{2} = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.754 |
|
|
\[ {}x^{2} y^{\prime }+2 x y = \sin \left (x \right ) \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.803 |
|
|
\[ {}x y^{\prime } = \sqrt {x}+3 y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.779 |
|
|
\[ {}\cos \left (x \right ) y^{\prime }+y \sin \left (x \right ) = \cos \left (x \right )^{2} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.528 |
|
|
\[ {}x y^{\prime }+\left (5 x +2\right ) y = \frac {20}{x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.84 |
|
|
\[ {}2 \sqrt {x}\, y^{\prime }+y = 2 x \,{\mathrm e}^{-\sqrt {x}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
3.005 |
|
|
\[ {}y^{\prime }-3 y = 6 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.473 |
|
|
\[ {}y^{\prime }-3 y = 6 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.214 |
|
|
\[ {}y^{\prime }+5 y = {\mathrm e}^{-3 x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.95 |
|
|
\[ {}x y^{\prime }+3 y = 20 x^{2} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.924 |
|
|
\[ {}x y^{\prime } = y+x^{2} \cos \left (x \right ) \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.349 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = x \left (3+3 x^{2}-y\right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.303 |
|
|
\[ {}y^{\prime }+6 x y = \sin \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.661 |
|
|
\[ {}x^{2} y^{\prime }+x y = \sqrt {x}\, \sin \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
5.733 |
|
|
\[ {}-y+x y^{\prime } = x^{2} {\mathrm e}^{-x^{2}} \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.387 |
|
|
\[ {}y^{\prime } = \frac {1}{\left (3 x +3 y+2\right )^{2}} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.151 |
|
|
\[ {}y^{\prime } = \frac {\left (3 x -2 y\right )^{2}+1}{3 x -2 y}+\frac {3}{2} \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.398 |
|
|
\[ {}\cos \left (-4 y+8 x -3\right ) y^{\prime } = 2+2 \cos \left (-4 y+8 x -3\right ) \] |
exact, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
42.072 |
|
|
\[ {}y^{\prime } = 1+\left (y-x \right )^{2} \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.104 |
|
|
\[ {}x^{2} y^{\prime }-x y = y^{2} \] |
riccati, bernoulli, exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.936 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\frac {x}{y} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.075 |
|
|
\[ {}\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right ) = 1+\sin \left (\frac {y}{x}\right ) \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.826 |
|
|
\[ {}y^{\prime } = \frac {x -y}{x +y} \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.326 |
|
|
\[ {}y^{\prime }+3 y = 3 y^{3} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.224 |
|
|
\[ {}y^{\prime }-\frac {3 y}{x} = \frac {y^{2}}{x^{2}} \] |
riccati, bernoulli, exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.058 |
|
|
\[ {}y^{\prime }+3 y \cot \left (x \right ) = 6 \cos \left (x \right ) y^{\frac {2}{3}} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
3.814 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = \frac {1}{y} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.112 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\frac {x^{2}}{y^{2}} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.426 |
|
|
\[ {}3 y^{\prime } = -2+\sqrt {2 x +3 y+4} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.576 |
|
|
\[ {}3 y^{\prime }+\frac {2 y}{x} = 4 \sqrt {y} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.432 |
|
|
\[ {}y^{\prime } = 4+\frac {1}{\sin \left (4 x -y\right )} \] |
exact, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.558 |
|
|
\[ {}\left (y-x \right ) y^{\prime } = 1 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.053 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = y \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.184 |
|
|
\[ {}\left (2 x y+2 x^{2}\right ) y^{\prime } = x^{2}+2 x y+2 y^{2} \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.078 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = x^{2} y^{3} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.13 |
|
|
\[ {}y^{\prime } = 2 \sqrt {2 x +y-3}-2 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.504 |
|
|
\[ {}y^{\prime } = 2 \sqrt {2 x +y-3} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
2.576 |
|
|
\[ {}-y+x y^{\prime } = \sqrt {x y+x^{2}} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.937 |
|
|
\[ {}y^{\prime }+3 y = \frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
1.609 |
|
|
\[ {}y^{\prime } = \left (x -y+3\right )^{2} \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.824 |
|
|
\[ {}y^{\prime }+2 x = 2 \sqrt {y+x^{2}} \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.547 |
|
|
|
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