Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.683 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.12 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.633 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.589 |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.651 |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = 0 \] |
1 |
1 |
1 |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.213 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.764 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 0 \] |
1 |
1 |
1 |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.608 |
|
|
\[ {}y^{\prime \prime }-x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.735 |
|
|
\[ {}y^{\prime \prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.128 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Lienard] |
✓ |
✓ |
1.317 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Hermite] |
✓ |
✓ |
1.102 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.14 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.138 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.951 |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.309 |
|
|
\[ {}y^{\prime \prime }-\left (1+x \right ) y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.353 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.9 |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.374 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.204 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.3 |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-\left (2-x \right ) y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.518 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.01 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.915 |
|
|
\[ {}y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.837 |
|
|
\[ {}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.603 |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
8.135 |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
15.289 |
|
|
\[ {}y^{\prime \prime }-x y = 1 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.869 |
|
|
\[ {}y^{\prime \prime }-4 x y^{\prime }-4 y = {\mathrm e}^{x} \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.461 |
|
|
\[ {}x y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.773 |
|
|
\[ {}y^{\prime \prime }+5 x y^{\prime }+\sqrt {x}\, y = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
8.385 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.865 |
|
|
\[ {}y^{\prime \prime }+y \cos \left (x \right ) = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.819 |
|
|
\[ {}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_Emden, _Fowler]] |
❇ |
N/A |
0.574 |
|
|
\[ {}x \left (x +3\right )^{2} y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.531 |
|
|
\[ {}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.377 |
|
|
\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (-1+x \right )^{3}} = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
9.521 |
|
|
\[ {}\left (x^{3}+4 x \right ) y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
11.376 |
|
|
\[ {}x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
11.011 |
|
|
\[ {}\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (-2+x \right ) y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.799 |
|
|
\[ {}x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
9.225 |
|
|
\[ {}x^{3} \left (x^{2}-25\right ) \left (-2+x \right )^{2} y^{\prime \prime }+3 x \left (-2+x \right ) y^{\prime }+7 \left (x +5\right ) y = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
6.977 |
|
|
\[ {}\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
10.585 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+5 \left (1+x \right ) y^{\prime }+\left (x^{2}-x \right ) y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.187 |
|
|
\[ {}x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
11.715 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.681 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.273 |
|
|
\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.345 |
|
|
\[ {}2 x y^{\prime \prime }+5 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.528 |
|
|
\[ {}4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.482 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.319 |
|
|
\[ {}3 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.54 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.386 |
|
|
\[ {}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[_Laguerre] |
✓ |
✓ |
3.592 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{9}\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.169 |
|
|
\[ {}9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.709 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.222 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.204 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.059 |
|
|
\[ {}x y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
9.587 |
|
|
\[ {}y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
8.763 |
|
|
\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.917 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.838 |
|
|
\[ {}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.729 |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+3 y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.42 |
|
|
\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{t}+\lambda y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.193 |
|
|
\[ {}x^{3} y^{\prime \prime }+y = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_Emden, _Fowler]] |
❇ |
N/A |
0.56 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_2nd_order, _exact, _linear, _homogeneous]] |
❇ |
N/A |
0.941 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0 \] |
1 |
1 |
1 |
second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.532 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0 \] |
1 |
1 |
1 |
second_order_bessel_ode |
[_Bessel] |
✓ |
✓ |
2.393 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.445 |
|
|
\[ {}16 x^{2} y^{\prime \prime }+16 x y^{\prime }+\left (16 x^{2}-1\right ) y = 0 \] |
1 |
1 |
1 |
second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.552 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
second_order_bessel_ode |
[_Lienard] |
✓ |
✓ |
2.19 |
|
|
\[ {}y^{\prime }+x y^{\prime \prime }+\left (x -\frac {4}{x}\right ) y = 0 \] |
1 |
1 |
1 |
second_order_bessel_ode |
[_Bessel] |
✓ |
✓ |
3.973 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y = 0 \] |
1 |
1 |
1 |
second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.443 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_bessel_ode, second_order_change_of_variable_on_y_method_1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.565 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y = 0 \] |
1 |
1 |
1 |
second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.171 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0 \] |
1 |
1 |
1 |
second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.941 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
second_order_bessel_ode |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.313 |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
second_order_bessel_ode |
[_Lienard] |
✓ |
✓ |
2.085 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
second_order_bessel_ode |
[_Lienard] |
✓ |
✓ |
2.316 |
|
|
\[ {}x y^{\prime \prime }-5 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
second_order_bessel_ode |
[_Lienard] |
✓ |
✓ |
2.46 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.976 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.57 |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_bessel_ode |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.591 |
|
|
\[ {}9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y = 0 \] |
1 |
1 |
1 |
second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.46 |
|
|
\[ {}y^{\prime \prime }-x^{2} y = 0 \] |
1 |
1 |
1 |
second_order_bessel_ode |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.303 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0 \] |
1 |
1 |
1 |
second_order_bessel_ode |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.395 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.682 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_bessel_ode, second_order_change_of_variable_on_y_method_1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.8 |
|
|
\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.677 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{2}+3\right ) y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_bessel_ode, second_order_change_of_variable_on_y_method_1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.508 |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.016 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.452 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }+3 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.828 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.98 |
|
|
\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[_Laguerre] |
✓ |
✓ |
1.625 |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.129 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.398 |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+3 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.838 |
|
|
\[ {}\left (1-2 \sin \left (x \right )\right ) y^{\prime \prime }+x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
12.342 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.143 |
|
|
\[ {}x y^{\prime \prime }+\left (1-\cos \left (x \right )\right ) y^{\prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
8.286 |
|
|
\[ {}\left ({\mathrm e}^{x}-1-x \right ) y^{\prime \prime }+x y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.122 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 10 x^{3}-2 x +5 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.0 |
|
|
\[ {}y^{\prime }-y = 1 \] |
1 |
1 |
1 |
first_order_laplace |
[_quadrature] |
✓ |
✓ |
0.418 |
|
|
\[ {}2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
first_order_laplace |
[_quadrature] |
✓ |
✓ |
0.335 |
|
|
\[ {}y^{\prime }+6 y = {\mathrm e}^{4 t} \] |
1 |
1 |
1 |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.526 |
|
|
\[ {}y^{\prime }-y = 2 \cos \left (5 t \right ) \] |
1 |
1 |
1 |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.654 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.44 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 6 \,{\mathrm e}^{3 t}-3 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.589 |
|
|
\[ {}y^{\prime \prime }+y = \sqrt {2}\, \sin \left (\sqrt {2}\, t \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.984 |
|
|
\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{t} \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.589 |
|
|
\[ {}2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y = {\mathrm e}^{-t} \] |
1 |
1 |
1 |
higher_order_laplace |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.052 |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = \sin \left (3 t \right ) \] |
1 |
1 |
1 |
higher_order_laplace |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.597 |
|
|
\[ {}y^{\prime }+y = {\mathrm e}^{-3 t} \cos \left (2 t \right ) \] |
1 |
1 |
1 |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.837 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.471 |
|
|
\[ {}y^{\prime }+4 y = {\mathrm e}^{-4 t} \] |
1 |
1 |
1 |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.501 |
|
|
\[ {}y^{\prime }-y = 1+t \,{\mathrm e}^{t} \] |
1 |
1 |
1 |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.519 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.439 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} {\mathrm e}^{2 t} \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.516 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = t \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.543 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = t^{3} \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.547 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 0 \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.441 |
|
|
\[ {}2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.586 |
|
|
\[ {}y^{\prime \prime }-y = {\mathrm e}^{t} \cos \left (t \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.731 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = t +1 \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.689 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.467 |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+20 y = 0 \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.286 |
|
|
\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \] |
1 |
1 |
1 |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.691 |
|
|
\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \] |
1 |
1 |
1 |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.87 |
|
|
\[ {}y^{\prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \] |
1 |
1 |
1 |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.791 |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.783 |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (t \right ) \operatorname {Heaviside}\left (t -2 \pi \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.107 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \operatorname {Heaviside}\left (-1+t \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.99 |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.503 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 1-\operatorname {Heaviside}\left (t -2\right )-\operatorname {Heaviside}\left (t -4\right )+\operatorname {Heaviside}\left (t -6\right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.454 |
|
|
\[ {}y^{\prime }+y = t \sin \left (t \right ) \] |
1 |
1 |
1 |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.716 |
|
|
\[ {}y^{\prime }-y = t \,{\mathrm e}^{t} \sin \left (t \right ) \] |
1 |
1 |
1 |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.717 |
|
|
\[ {}y^{\prime \prime }+9 y = \cos \left (3 t \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.723 |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (t \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.665 |
|
|
\[ {}y^{\prime \prime }+16 y = \left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.734 |
|
|
\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} 1 & 0\le t <\frac {\pi }{2} \\ \sin \left (t \right ) & \frac {\pi }{2}\le t \end {array}\right . \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.712 |
|
|
\[ {}t y^{\prime \prime }-y^{\prime } = 2 t^{2} \] |
1 |
1 |
1 |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.659 |
|
|
\[ {}2 y^{\prime \prime }+t y^{\prime }-2 y = 10 \] |
1 |
0 |
1 |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.484 |
|
|
\[ {}y^{\prime \prime }+y = \sin \left (t \right )+t \sin \left (t \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.809 |
|
|
\[ {}y^{\prime }-3 y = \delta \left (t -2\right ) \] |
1 |
1 |
1 |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.638 |
|
|
\[ {}y^{\prime }+y = \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.637 |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.537 |
|
|
\[ {}y^{\prime \prime }+16 y = \delta \left (t -2 \pi \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.519 |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.66 |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.652 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.613 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 1+\delta \left (t -2\right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.87 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -2 \pi \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.724 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = \delta \left (-1+t \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.547 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.013 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.358 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.475 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.496 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x-5 y \\ y^{\prime }=4 x+8 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.996 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-7 y \\ y^{\prime }=5 x \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.978 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+4 y-9 z \\ y^{\prime }=6 x-y \\ z^{\prime }=10 x+4 y+3 z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
23.392 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+2 z \\ z^{\prime }=-x+z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
18.528 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-y+z+t -1 \\ y^{\prime }=2 x+y-z-3 t^{2} \\ z^{\prime }=x+y+z+t^{2}-t +2 \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
11.493 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+4 y+{\mathrm e}^{-t} \sin \left (2 t \right ) \\ y^{\prime }=5 x+9 z+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \\ z^{\prime }=y+6 z-{\mathrm e}^{-t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
301.921 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x+2 y+{\mathrm e}^{t} \\ y^{\prime }=-x+3 y-{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.681 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=7 x+5 y-9 z-8 \,{\mathrm e}^{-2 t} \\ y^{\prime }=4 x+y+z+2 \,{\mathrm e}^{5 t} \\ z^{\prime }=-2 y+3 z+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
117.423 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-y+2 z+{\mathrm e}^{-t}-3 t \\ y^{\prime }=3 x-4 y+z+2 \,{\mathrm e}^{-t}+t \\ z^{\prime }=-2 x+5 y+6 z+2 \,{\mathrm e}^{-t}-t \end {array}\right ] \] |
1 |
1 |
0 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
208.704 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x-7 y+4 \sin \left (t \right )+\left (t -4\right ) {\mathrm e}^{4 t} \\ y^{\prime }=x+y+8 \sin \left (t \right )+\left (1+2 t \right ) {\mathrm e}^{4 t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
9.974 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x-4 y \\ y^{\prime }=4 x-7 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.529 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x+5 y \\ y^{\prime }=-2 x+4 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.688 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+\frac {y}{4} \\ y^{\prime }=x-y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.477 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.49 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y+z \\ y^{\prime }=6 x-y \\ z^{\prime }=-x-2 y-z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.94 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=z+x \\ y^{\prime }=x+y \\ z^{\prime }=-2 x-z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.938 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=4 x+3 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.464 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=x+3 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.447 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-4 x+2 y \\ y^{\prime }=-\frac {5 x}{2}+2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.509 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-\frac {5 x}{2}+2 y \\ y^{\prime }=\frac {3 x}{4}-2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.494 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=10 x-5 y \\ y^{\prime }=8 x-12 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.517 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-6 x+2 y \\ y^{\prime }=-3 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.441 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+y-z \\ y^{\prime }=2 y \\ z^{\prime }=y-z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.622 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x-7 y \\ y^{\prime }=5 x+10 y+4 z \\ z^{\prime }=5 y+2 z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.806 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+y \\ y^{\prime }=x+2 y+z \\ z^{\prime }=3 y-z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.794 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=z+x \\ y^{\prime }=y \\ z^{\prime }=z+x \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.533 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x-y \\ y^{\prime }=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\ z^{\prime }=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.841 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x-y \\ y^{\prime }=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\ z^{\prime }=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.736 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+4 y+2 z \\ y^{\prime }=4 x-y-2 z \\ z^{\prime }=6 z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.751 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=\frac {x}{2} \\ y^{\prime }=x-\frac {y}{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.385 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+y+4 z \\ y^{\prime }=2 y \\ z^{\prime }=x+y+z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.66 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=\frac {9 x}{10}+\frac {21 y}{10}+\frac {16 z}{5} \\ y^{\prime }=\frac {7 x}{10}+\frac {13 y}{2}+\frac {21 z}{5} \\ z^{\prime }=\frac {11 x}{10}+\frac {17 y}{10}+\frac {17 z}{5} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
95.264 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{3}-\frac {9 x_{4}}{5} \\ x_{2}^{\prime }=\frac {51 x_{2}}{10}-x_{4}+3 x_{5} \\ x_{3}^{\prime }=x_{1}+2 x_{2}-3 x_{3} \\ x_{4}^{\prime }=x_{2}-\frac {31 x_{3}}{10}+4 x_{4} \\ x_{5}^{\prime }=-\frac {14 x_{1}}{5}+\frac {3 x_{4}}{2}-x_{5} \end {array}\right ] \] |
1 |
1 |
5 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
151.959 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=9 x-3 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.371 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-6 x+5 y \\ y^{\prime }=-5 x+4 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.497 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+3 y \\ y^{\prime }=-3 x+5 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.52 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=12 x-9 y \\ y^{\prime }=4 x \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.522 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x-y-z \\ y^{\prime }=x+y-z \\ z^{\prime }=x-y+z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.678 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x+2 y+4 z \\ y^{\prime }=2 x+2 z \\ z^{\prime }=4 x+2 y+3 z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.77 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=5 x-4 y \\ y^{\prime }=x+2 z \\ z^{\prime }=2 y+5 z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.576 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=3 y+z \\ z^{\prime }=-y+z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.624 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x+2 y-z \\ z^{\prime }=y \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.434 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x+y \\ y^{\prime }=4 y+z \\ z^{\prime }=4 z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.366 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+4 y \\ y^{\prime }=-x+6 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.464 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=z \\ y^{\prime }=y \\ z^{\prime }=x \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.489 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=6 x-y \\ y^{\prime }=5 x+2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.692 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x-y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.588 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=5 x+y \\ y^{\prime }=-2 x+3 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.664 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x+5 y \\ y^{\prime }=-2 x+6 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.743 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-5 y \\ y^{\prime }=5 x-4 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.663 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-8 y \\ y^{\prime }=x-3 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.687 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=z \\ y^{\prime }=-z \\ z^{\prime }=y \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.654 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y+2 z \\ y^{\prime }=3 x+6 z \\ z^{\prime }=-4 x-3 z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.451 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-12 y-14 z \\ y^{\prime }=x+2 y-3 z \\ z^{\prime }=x+y-2 z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.919 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+3 y-7 \\ y^{\prime }=-x-2 y+5 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.918 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=5 x+9 y+2 \\ y^{\prime }=-x+11 y+6 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.015 |
|
|
|
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