|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime } = \sin \left (x \right )^{4} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
2.008 |
|
|
\[ {}y^{\prime \prime \prime \prime }+\frac {25 y^{\prime \prime }}{2}-5 y^{\prime }+\frac {629 y}{16} = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
2.489 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=-4 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.619 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-5 x+4 y \\ y^{\prime }=2 x+2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.734 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.975 |
|
|
\[ {}y^{\prime }-y = \sin \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.642 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.43 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+45 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.921 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-16 y = 0 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_Emden, _Fowler]] |
✓ |
✓ |
5.091 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 0 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.804 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = x \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.148 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = 2 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.668 |
|
|
\[ {}2 x -3 y+\left (2 y-3 x \right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.77 |
|
|
\[ {}y \cos \left (x y\right )+\sin \left (x \right )+x \cos \left (x y\right ) y^{\prime } = 0 \] |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
9.581 |
|
|
\[ {}y^{\prime } = x \,{\mathrm e}^{-x^{2}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.276 |
|
|
\[ {}y^{\prime } = x^{2} \sin \left (x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.842 |
|
|
\[ {}y^{\prime } = \frac {2 x^{2}-x +1}{\left (-1+x \right ) \left (x^{2}+1\right )} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.423 |
|
|
\[ {}y^{\prime } = \frac {x^{2}}{\sqrt {x^{2}-1}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.605 |
|
|
\[ {}y^{\prime }+2 y = x^{2} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.708 |
|
|
\[ {}y^{\prime \prime }+4 y = t \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
1.134 |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.826 |
|
|
\[ {}y^{\prime } = \cos \left (x \right )^{2} \sin \left (x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.403 |
|
|
\[ {}y^{\prime } = \frac {4 x -9}{3 \left (x -3\right )^{\frac {2}{3}}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.024 |
|
|
\[ {}y^{\prime }+t^{2} = y^{2} \] |
riccati |
[_Riccati] |
✗ |
N/A |
3.217 |
|
|
\[ {}y^{\prime }+t^{2} = \frac {1}{y^{2}} \] |
unknown |
[_rational] |
❇ |
N/A |
1.046 |
|
|
\[ {}y^{\prime } = y+\frac {1}{1-t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.396 |
|
|
\[ {}y^{\prime } = y^{\frac {1}{5}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.817 |
|
|
\[ {}\frac {y^{\prime }}{t} = \sqrt {y} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.411 |
|
|
\[ {}y^{\prime } = 4 t^{2}-t y^{2} \] |
riccati |
[_Riccati] |
✓ |
✓ |
9.375 |
|
|
\[ {}y^{\prime } = y \sqrt {t} \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.45 |
|
|
\[ {}y^{\prime } = 6 y^{\frac {2}{3}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.816 |
|
|
\[ {}y^{\prime } = \sin \left (y\right )-\cos \left (t \right ) \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
2.324 |
|
|
\[ {}t y^{\prime } = y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.45 |
|
|
\[ {}y^{\prime } = y \tan \left (t \right ) \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.138 |
|
|
\[ {}y^{\prime } = \frac {1}{t^{2}+1} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.68 |
|
|
\[ {}y^{\prime } = \sqrt {y^{2}-1} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
2.811 |
|
|
\[ {}y^{\prime } = \sqrt {y^{2}-1} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.481 |
|
|
\[ {}y^{\prime } = \sqrt {y^{2}-1} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
4.001 |
|
|
\[ {}y^{\prime } = \sqrt {y^{2}-1} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.434 |
|
|
\[ {}y^{\prime } = \sqrt {25-y^{2}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
2.458 |
|
|
\[ {}y^{\prime } = \sqrt {25-y^{2}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.438 |
|
|
\[ {}y^{\prime } = \sqrt {25-y^{2}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
3.124 |
|
|
\[ {}y^{\prime } = \sqrt {25-y^{2}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.451 |
|
|
\[ {}t y^{\prime }+y = t^{3} \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.257 |
|
|
\[ {}t^{3} y^{\prime }+t^{4} y = 2 t^{3} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.265 |
|
|
\[ {}2 y^{\prime }+t y = \ln \left (t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
5.365 |
|
|
\[ {}y^{\prime }+y \sec \left (t \right ) = t \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
5.944 |
|
|
\[ {}y^{\prime }+\frac {y}{t -3} = \frac {1}{-1+t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.927 |
|
|
\[ {}\left (t -2\right ) y^{\prime }+\left (t^{2}-4\right ) y = \frac {1}{2+t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
8.855 |
|
|
\[ {}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
5.844 |
|
|
\[ {}y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}} = t \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
7.891 |
|
|
\[ {}t y^{\prime }+y = t \sin \left (t \right ) \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.056 |
|
|
\[ {}y^{\prime }+y \tan \left (t \right ) = \sin \left (t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.844 |
|
|
\[ {}y^{\prime } = y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.44 |
|
|
\[ {}y^{\prime } = t y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.537 |
|
|
\[ {}y^{\prime } = -\frac {t}{y} \] |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
20.007 |
|
|
\[ {}y^{\prime } = -y^{3} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.509 |
|
|
\[ {}y^{\prime } = \frac {x}{y^{2}} \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
6.905 |
|
|
\[ {}\frac {1}{2 \sqrt {t}}+y^{2} y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.367 |
|
|
\[ {}y^{\prime } = \frac {\sqrt {y}}{x^{2}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.974 |
|
|
\[ {}y^{\prime } = \frac {1+y^{2}}{y} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.663 |
|
|
\[ {}6+4 t^{3}+\left (5+\frac {9}{y^{8}}\right ) y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.216 |
|
|
\[ {}\frac {6}{t^{9}}-\frac {6}{t^{3}}+t^{7}+\left (9+\frac {1}{s^{2}}-4 s^{8}\right ) s^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.842 |
|
|
\[ {}4 \sinh \left (4 y\right ) y^{\prime } = 6 \cosh \left (3 x \right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
7.496 |
|
|
\[ {}y^{\prime } = \frac {y+1}{t +1} \] |
exact, linear, separable, homogeneousTypeD2, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.514 |
|
|
\[ {}y^{\prime } = \frac {y+2}{1+2 t} \] |
exact, linear, separable, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.882 |
|
|
\[ {}\frac {3}{t^{2}} = \left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime } \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.525 |
|
|
\[ {}3 \sin \left (x \right )-4 \cos \left (y\right ) y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.569 |
|
|
\[ {}\cos \left (y\right ) y^{\prime } = 8 \sin \left (8 t \right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.514 |
|
|
\[ {}y^{\prime }+k y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.725 |
|
|
\[ {}\left (5 x^{5}-4 \cos \left (x\right )\right ) x^{\prime }+2 \cos \left (9 t \right )+2 \sin \left (7 t \right ) = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
38.446 |
|
|
\[ {}\cosh \left (6 t \right )+5 \sinh \left (4 t \right )+20 \sinh \left (y\right ) y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
10.86 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{2 y+10 t} \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.952 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{3 y+2 t} \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.931 |
|
|
\[ {}\sin \left (t \right )^{2} = \cos \left (y\right )^{2} y^{\prime } \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.695 |
|
|
\[ {}3 \sin \left (t \right )-\sin \left (3 t \right ) = \left (\cos \left (4 y\right )-4 \cos \left (y\right )\right ) y^{\prime } \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
36.885 |
|
|
\[ {}x^{\prime } = \frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
35.875 |
|
|
\[ {}\left (2-\frac {5}{y^{2}}\right ) y^{\prime }+4 \cos \left (x \right )^{2} = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.216 |
|
|
\[ {}y^{\prime } = \frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}} \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
3.423 |
|
|
\[ {}\tan \left (y\right ) \sec \left (y\right )^{2} y^{\prime }+\cos \left (2 x \right )^{3} \sin \left (2 x \right ) = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
37.102 |
|
|
\[ {}y^{\prime } = \frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.635 |
|
|
\[ {}x \sin \left (x^{2}\right ) = \frac {\cos \left (\sqrt {y}\right ) y^{\prime }}{\sqrt {y}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
37.088 |
|
|
\[ {}\frac {-2+x}{x^{2}-4 x +3} = \frac {\left (1-\frac {1}{y}\right )^{2} y^{\prime }}{y^{2}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
10.648 |
|
|
\[ {}\frac {\cos \left (y\right ) y^{\prime }}{\left (1-\sin \left (y\right )\right )^{2}} = \sin \left (x \right )^{3} \cos \left (x \right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
37.259 |
|
|
\[ {}y^{\prime } = \frac {\left (5-2 \cos \left (x \right )\right )^{3} \sin \left (x \right ) \cos \left (y\right )^{4}}{\sin \left (y\right )} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
36.439 |
|
|
\[ {}\frac {\sqrt {\ln \left (x \right )}}{x} = \frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.431 |
|
|
\[ {}y^{\prime } = \frac {5^{-t}}{y^{2}} \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
50.23 |
|
|
\[ {}y^{\prime } = t^{2} y^{2}+y^{2}-t^{2}-1 \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.637 |
|
|
\[ {}y^{\prime } = y^{2}-3 y+2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.855 |
|
|
\[ {}4 \left (-1+x \right )^{2} y^{\prime }-3 \left (3+y\right )^{2} = 0 \] |
exact, riccati, separable, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.885 |
|
|
\[ {}y^{\prime } = \sin \left (t -y\right )+\sin \left (t +y\right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.093 |
|
|
\[ {}y^{\prime } = y^{3}+1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
4.538 |
|
|
\[ {}y^{\prime } = y^{3}-1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
4.643 |
|
|
\[ {}y^{\prime } = y^{3}+y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
2.178 |
|
|
\[ {}y^{\prime } = y^{3}-y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.717 |
|
|
\[ {}y^{\prime } = y^{3}-y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.527 |
|
|
\[ {}y^{\prime } = y^{3}+y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.966 |
|
|
\[ {}y^{\prime } = x^{3} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.317 |
|
|
\[ {}y^{\prime } = \cos \left (t \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.51 |
|
|
\[ {}1 = \cos \left (y\right ) y^{\prime } \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.472 |
|
|
|
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