|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 5 \cos \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.452 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.498 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 2 \sin \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.452 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.493 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = -4 \cos \left (3 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.553 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 3 \cos \left (2 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.849 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -\cos \left (5 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.064 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.901 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = \cos \left (3 t \right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.707 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.742 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.778 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.94 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 \cos \left (2 t \right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.108 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+y = \cos \left (3 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.755 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.944 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.785 |
|
|
\[ {}y^{\prime \prime }+9 y = \cos \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.794 |
|
|
\[ {}y^{\prime \prime }+9 y = 5 \sin \left (2 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.715 |
|
|
\[ {}y^{\prime \prime }+4 y = -\cos \left (\frac {t}{2}\right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.859 |
|
|
\[ {}y^{\prime \prime }+4 y = 3 \cos \left (2 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.643 |
|
|
\[ {}y^{\prime \prime }+9 y = 2 \cos \left (3 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.651 |
|
|
\[ {}y^{\prime \prime }+4 y = 8 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.468 |
|
|
\[ {}y^{\prime \prime }-4 y = {\mathrm e}^{2 t} \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.497 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 2 \,{\mathrm e}^{t} \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.613 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (t -4\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.898 |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (2 t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.609 |
|
|
\[ {}y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.593 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.691 |
|
|
\[ {}y^{\prime \prime }+3 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.58 |
|
|
\[ {}y^{\prime \prime }+3 y = 5 \delta \left (t -2\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.171 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -3\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.632 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = -2 \delta \left (t -2\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.563 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (-1+t \right )-3 \delta \left (t -4\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
5.292 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = {\mathrm e}^{-2 t} \sin \left (4 t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.986 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.886 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.871 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.797 |
|
|
\[ {}y^{\prime \prime }+16 y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.408 |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.676 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.38 |
|
|
\[ {}y^{\prime \prime }+16 y = t \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.548 |
|
|
\[ {}y^{\prime } = 3-\sin \left (x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.297 |
|
|
\[ {}y^{\prime } = 3-\sin \left (y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.417 |
|
|
\[ {}y^{\prime }+4 y = {\mathrm e}^{2 x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.718 |
|
|
\[ {}x y^{\prime } = \arcsin \left (x^{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.474 |
|
|
\[ {}y y^{\prime } = 2 x \] |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.46 |
|
|
\[ {}y^{\prime \prime } = \frac {1+x}{-1+x} \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_quadrature, second_order_linear_constant_coeff |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.842 |
|
|
\[ {}x^{2} y^{\prime \prime } = 1 \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_quadrature, second_order_linear_constant_coeff |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.615 |
|
|
\[ {}y^{2} y^{\prime \prime } = 8 x^{2} \] |
unknown |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
0.096 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+8 y = {\mathrm e}^{-x^{2}} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.121 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime } = 0 \] |
kovacic, second_order_euler_ode, second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.748 |
|
|
\[ {}y^{\prime } = 4 x^{3} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.131 |
|
|
\[ {}y^{\prime } = 20 \,{\mathrm e}^{-4 x} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.154 |
|
|
\[ {}x y^{\prime }+\sqrt {x} = 2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.186 |
|
|
\[ {}\sqrt {x +4}\, y^{\prime } = 1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.21 |
|
|
\[ {}y^{\prime } = x \cos \left (x^{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.584 |
|
|
\[ {}y^{\prime } = x \cos \left (x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.343 |
|
|
\[ {}x = \left (x^{2}-9\right ) y^{\prime } \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.208 |
|
|
\[ {}1 = \left (x^{2}-9\right ) y^{\prime } \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.185 |
|
|
\[ {}1 = x^{2}-9 y^{\prime } \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.128 |
|
|
\[ {}y^{\prime \prime } = \sin \left (2 x \right ) \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_quadrature, second_order_linear_constant_coeff |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.073 |
|
|
\[ {}y^{\prime \prime }-3 = x \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_quadrature, second_order_linear_constant_coeff |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.625 |
|
|
\[ {}y^{\prime \prime \prime \prime } = 1 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _quadrature]] |
✓ |
✓ |
0.167 |
|
|
\[ {}y^{\prime } = 40 \,{\mathrm e}^{2 x} x \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.306 |
|
|
\[ {}\left (x +6\right )^{\frac {1}{3}} y^{\prime } = 1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.466 |
|
|
\[ {}y^{\prime } = \frac {-1+x}{1+x} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.348 |
|
|
\[ {}x y^{\prime }+2 = \sqrt {x} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.448 |
|
|
\[ {}\cos \left (x \right ) y^{\prime }-\sin \left (x \right ) = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.556 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = 1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.315 |
|
|
\[ {}x y^{\prime \prime }+2 = \sqrt {x} \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_quadrature, second_order_linear_constant_coeff |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.524 |
|
|
\[ {}y^{\prime } = \sin \left (\frac {x}{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.315 |
|
|
\[ {}y^{\prime } = \sin \left (\frac {x}{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.232 |
|
|
\[ {}y^{\prime } = \sin \left (\frac {x}{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.248 |
|
|
\[ {}y^{\prime } = 3 \sqrt {x +3} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.194 |
|
|
\[ {}y^{\prime } = 3 \sqrt {x +3} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.332 |
|
|
\[ {}y^{\prime } = 3 \sqrt {x +3} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.327 |
|
|
\[ {}y^{\prime } = 3 \sqrt {x +3} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.33 |
|
|
\[ {}y^{\prime } = x \,{\mathrm e}^{-x^{2}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.303 |
|
|
\[ {}y^{\prime } = \frac {x}{\sqrt {x^{2}+5}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.431 |
|
|
\[ {}y^{\prime } = \frac {1}{x^{2}+1} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.294 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{-9 x^{2}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.341 |
|
|
\[ {}x y^{\prime } = \sin \left (x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.474 |
|
|
\[ {}x y^{\prime } = \sin \left (x^{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.56 |
|
|
\[ {}y^{\prime } = \left \{\begin {array}{cc} 0 & x <0 \\ 1 & 0\le x \end {array}\right . \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.516 |
|
|
\[ {}y^{\prime } = \left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x \end {array}\right . \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.596 |
|
|
\[ {}y^{\prime } = \left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x <2 \\ 0 & 2\le x \end {array}\right . \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.693 |
|
|
\[ {}y^{\prime }+3 x y = 6 x \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.275 |
|
|
\[ {}\sin \left (x +y\right )-y y^{\prime } = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
1.979 |
|
|
\[ {}y^{\prime }-y^{3} = 8 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
3.319 |
|
|
\[ {}x^{2} y^{\prime }+x y^{2} = x \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.619 |
|
|
\[ {}y^{\prime }-y^{2} = x \] |
riccati |
[[_Riccati, _special]] |
✓ |
✓ |
0.812 |
|
|
\[ {}y^{3}-25 y+y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
3.358 |
|
|
\[ {}\left (-2+x \right ) y^{\prime } = 3+y \] |
exact, linear, separable, homogeneousTypeD2, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.36 |
|
|
\[ {}\left (y-2\right ) y^{\prime } = x -3 \] |
exact, separable, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.321 |
|
|
\[ {}y^{\prime }+2 y-y^{2} = -2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.35 |
|
|
\[ {}y^{\prime }+\left (8-x \right ) y-y^{2} = -8 x \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.43 |
|
|
\[ {}y^{\prime } = 2 \sqrt {y} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.325 |
|
|
\[ {}y^{\prime } = 3 y^{2}-y^{2} \sin \left (x \right ) \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.945 |
|
|
\[ {}y^{\prime } = 3 x -y \sin \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.444 |
|
|
\[ {}x y^{\prime } = \left (x -y\right )^{2} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.31 |
|
|
|
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