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) |
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.385 |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.24 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.628 |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-\left (2+x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.624 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[_Gegenbauer] |
✓ |
✓ |
0.609 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[_Gegenbauer] |
✓ |
✓ |
0.595 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.702 |
|
|
\[ {}5 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime } = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.299 |
|
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+16 y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.394 |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.116 |
|
|
\[ {}9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime } = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.38 |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.438 |
|
|
\[ {}y^{\prime \prime \prime \prime }-16 y^{\prime \prime }+16 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.634 |
|
|
\[ {}y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.141 |
|
|
\[ {}6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.583 |
|
|
\[ {}y^{\prime \prime \prime \prime } = 16 y \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.418 |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.352 |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.165 |
|
|
\[ {}2 y^{\prime \prime \prime }-3 y^{\prime \prime }-2 y^{\prime } = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.585 |
|
|
\[ {}3 y^{\prime \prime \prime }+2 y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.508 |
|
|
\[ {}y^{\prime \prime \prime }+10 y^{\prime \prime }+25 y^{\prime } = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.664 |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.365 |
|
|
\[ {}2 y^{\prime \prime \prime }-y^{\prime \prime }-5 y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.309 |
|
|
\[ {}y^{\prime \prime \prime }+27 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.573 |
|
|
\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-6 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.5 |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.425 |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.123 |
|
|
\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+100 y^{\prime }-500 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.813 |
|
|
\[ {}y^{\prime \prime \prime } = y \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
1.059 |
|
|
\[ {}y^{\prime \prime \prime \prime } = y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+2 y \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
1.063 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime } = 0 \] |
1 |
1 |
1 |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.557 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+x y^{\prime } = 0 \] |
1 |
1 |
1 |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.668 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+x y^{\prime } = 0 \] |
1 |
1 |
1 |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.49 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+x y^{\prime } = 0 \] |
1 |
1 |
1 |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.724 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.232 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=6 x_{1} \\ x_{2}^{\prime }=-3 x_{1}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.468 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }=-3 x_{1}+4 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.549 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.469 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+3 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.518 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+4 x_{2} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.482 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2} \\ x_{2}^{\prime }=6 x_{1}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.541 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=6 x_{1}-7 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.505 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}+5 x_{2} \\ x_{2}^{\prime }=-6 x_{1}-2 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.477 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }=6 x_{1}-5 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.551 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.687 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.577 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=9 x_{1}+3 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.689 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.482 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.77 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-9 x_{2} \\ x_{2}^{\prime }=2 x_{1}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.8 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}+3 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.64 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-5 x_{2} \\ x_{2}^{\prime }=4 x_{1}+3 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.782 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-50 x_{1}+20 x_{2} \\ x_{2}^{\prime }=100 x_{1}-60 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.555 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2}+4 x_{3} \\ x_{2}^{\prime }=x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }=4 x_{1}+x_{2}+4 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.752 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }=2 x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}+7 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.745 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+4 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2}+4 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.74 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }=x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }=3 x_{1}+x_{2}+5 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.76 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-6 x_{3} \\ x_{2}^{\prime }=2 x_{1}-x_{2}-2 x_{3} \\ x_{3}^{\prime }=4 x_{1}-2 x_{2}-4 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.834 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-5 x_{1}-4 x_{2}-2 x_{3} \\ x_{3}^{\prime }=5 x_{1}+5 x_{2}+3 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.816 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=-5 x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }=5 x_{1}+5 x_{2}+3 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.801 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }=-4 x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }=4 x_{1}+4 x_{2}+2 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.106 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+5 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-6 x_{1}-6 x_{2}-5 x_{3} \\ x_{3}^{\prime }=6 x_{1}+6 x_{2}+5 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.207 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{3} \\ x_{2}^{\prime }=9 x_{1}-x_{2}+2 x_{3} \\ x_{3}^{\prime }=-9 x_{1}+4 x_{2}-x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.155 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=2 x_{1}+2 x_{2} \\ x_{3}^{\prime }=3 x_{2}+3 x_{3} \\ x_{4}^{\prime }=4 x_{3}+4 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.102 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+9 x_{4} \\ x_{2}^{\prime }=4 x_{1}+2 x_{2}-10 x_{4} \\ x_{3}^{\prime }=-x_{3}+8 x_{4} \\ x_{4}^{\prime }=x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.089 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\ x_{3}^{\prime }=5 x_{3} \\ x_{4}^{\prime }=-21 x_{3}-2 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.135 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2}+x_{3}+7 x_{4} \\ x_{2}^{\prime }=x_{1}+4 x_{2}+10 x_{3}+x_{4} \\ x_{3}^{\prime }=x_{1}+10 x_{2}+4 x_{3}+x_{4} \\ x_{4}^{\prime }=7 x_{1}+x_{2}+x_{3}+4 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.414 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-40 x_{1}-12 x_{2}+54 x_{3} \\ x_{2}^{\prime }=35 x_{1}+13 x_{2}-46 x_{3} \\ x_{3}^{\prime }=-25 x_{1}-7 x_{2}+34 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.879 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-20 x_{1}+11 x_{2}+13 x_{3} \\ x_{2}^{\prime }=12 x_{1}-x_{2}-7 x_{3} \\ x_{3}^{\prime }=-48 x_{1}+21 x_{2}+31 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.928 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=147 x_{1}+23 x_{2}-202 x_{3} \\ x_{2}^{\prime }=-90 x_{1}-9 x_{2}+129 x_{3} \\ x_{3}^{\prime }=90 x_{1}+15 x_{2}-123 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.966 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}-7 x_{2}-5 x_{3} \\ x_{2}^{\prime }=-12 x_{1}+7 x_{2}+11 x_{3}+9 x_{4} \\ x_{3}^{\prime }=24 x_{1}-17 x_{2}-19 x_{3}-9 x_{4} \\ x_{4}^{\prime }=-18 x_{1}+13 x_{2}+17 x_{3}+9 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.44 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=13 x_{1}-42 x_{2}+106 x_{3}+139 x_{4} \\ x_{2}^{\prime }=2 x_{1}-16 x_{2}+52 x_{3}+70 x_{4} \\ x_{3}^{\prime }=x_{1}+6 x_{2}-20 x_{3}-31 x_{4} \\ x_{4}^{\prime }=-x_{1}-6 x_{2}+22 x_{3}+33 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.939 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=23 x_{1}-18 x_{2}-16 x_{3} \\ x_{2}^{\prime }=-8 x_{1}+6 x_{2}+7 x_{3}+9 x_{4} \\ x_{3}^{\prime }=34 x_{1}-27 x_{2}-26 x_{3}-9 x_{4} \\ x_{4}^{\prime }=-26 x_{1}+21 x_{2}+25 x_{3}+12 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.567 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=47 x_{1}-8 x_{2}+5 x_{3}-5 x_{4} \\ x_{2}^{\prime }=-10 x_{1}+32 x_{2}+18 x_{3}-2 x_{4} \\ x_{3}^{\prime }=139 x_{1}-40 x_{2}-167 x_{3}-121 x_{4} \\ x_{4}^{\prime }=-232 x_{1}+64 x_{2}+360 x_{3}+248 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.708 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=139 x_{1}-14 x_{2}-52 x_{3}-14 x_{4}+28 x_{5} \\ x_{2}^{\prime }=-22 x_{1}+5 x_{2}+7 x_{3}+8 x_{4}-7 x_{5} \\ x_{3}^{\prime }=370 x_{1}-38 x_{2}-139 x_{3}-38 x_{4}+76 x_{5} \\ x_{4}^{\prime }=152 x_{1}-16 x_{2}-59 x_{3}-13 x_{4}+35 x_{5} \\ x_{5}^{\prime }=95 x_{1}-10 x_{2}-38 x_{3}-7 x_{4}+23 x_{5} \end {array}\right ] \] |
1 |
1 |
5 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.461 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}+13 x_{2}-13 x_{6} \\ x_{2}^{\prime }=-14 x_{1}+19 x_{2}-10 x_{3}-20 x_{4}+10 x_{5}+4 x_{6} \\ x_{3}^{\prime }=-30 x_{1}+12 x_{2}-7 x_{3}-30 x_{4}+12 x_{5}+18 x_{6} \\ x_{4}^{\prime }=-12 x_{1}+10 x_{2}-10 x_{3}-9 x_{4}+10 x_{5}+2 x_{6} \\ x_{5}^{\prime }=6 x_{1}+9 x_{2}+6 x_{4}+5 x_{5}-15 x_{6} \\ x_{6}^{\prime }=-14 x_{1}+23 x_{2}-10 x_{3}-20 x_{4}+10 x_{5} \end {array}\right ] \] |
1 |
1 |
6 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
4.611 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}+4 x_{2} \\ x_{2}^{\prime }=-6 x_{1}-x_{2} \\ x_{3}^{\prime }=6 x_{1}+4 x_{2}+3 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.8 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2} \\ x_{2}^{\prime }=3 x_{1}+7 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.557 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+2 x_{3} \\ x_{2}^{\prime }=-5 x_{1}-3 x_{2}-7 x_{3} \\ x_{3}^{\prime }=x_{1} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.62 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{3} \\ x_{2}^{\prime }=x_{4} \\ x_{3}^{\prime }=-2 x_{1}+2 x_{2}-3 x_{3}+x_{4} \\ x_{4}^{\prime }=2 x_{1}-2 x_{2}+x_{3}-3 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.855 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2} \\ x_{2}^{\prime }=-x_{1}-4 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.535 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.51 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+5 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.55 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+5 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.523 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}+x_{2} \\ x_{2}^{\prime }=-4 x_{1}+3 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.578 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}+9 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.546 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=-7 x_{1}+9 x_{2}+7 x_{3} \\ x_{3}^{\prime }=2 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.431 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=25 x_{1}+12 x_{2} \\ x_{2}^{\prime }=-18 x_{1}-5 x_{2} \\ x_{3}^{\prime }=6 x_{1}+6 x_{2}+13 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.778 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-19 x_{1}+12 x_{2}+84 x_{3} \\ x_{2}^{\prime }=5 x_{2} \\ x_{3}^{\prime }=-8 x_{1}+4 x_{2}+33 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.8 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-13 x_{1}+40 x_{2}-48 x_{3} \\ x_{2}^{\prime }=-8 x_{1}+23 x_{2}-24 x_{3} \\ x_{3}^{\prime }=3 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.809 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-4 x_{3} \\ x_{2}^{\prime }=-x_{1}-x_{2}-x_{3} \\ x_{3}^{\prime }=x_{1}+x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.492 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{3} \\ x_{2}^{\prime }=-x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}-x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.459 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{3} \\ x_{2}^{\prime }=x_{2}-4 x_{3} \\ x_{3}^{\prime }=x_{2}-3 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.447 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{3} \\ x_{2}^{\prime }=-5 x_{1}-x_{2}-5 x_{3} \\ x_{3}^{\prime }=4 x_{1}+x_{2}-2 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.579 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-9 x_{2} \\ x_{2}^{\prime }=x_{1}+4 x_{2} \\ x_{3}^{\prime }=x_{1}+3 x_{2}+x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.54 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2}-3 x_{3} \\ x_{3}^{\prime }=2 x_{1}+3 x_{2}+4 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.511 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=18 x_{1}+7 x_{2}+4 x_{3} \\ x_{3}^{\prime }=-27 x_{1}-9 x_{2}-5 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.549 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=x_{1}+3 x_{2}+x_{3} \\ x_{3}^{\prime }=-2 x_{1}-4 x_{2}-x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.509 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2}-2 x_{4} \\ x_{2}^{\prime }=x_{2} \\ x_{3}^{\prime }=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\ x_{4}^{\prime }=-4 x_{2}-x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.004 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+x_{4} \\ x_{2}^{\prime }=2 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{3}+x_{4} \\ x_{4}^{\prime }=2 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.569 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \\ x_{3}^{\prime }=x_{1}+2 x_{2}+x_{3} \\ x_{4}^{\prime }=x_{2}+x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.523 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+3 x_{2}+7 x_{3} \\ x_{2}^{\prime }=-x_{2}-4 x_{3} \\ x_{3}^{\prime }=x_{2}+3 x_{3} \\ x_{4}^{\prime }=-6 x_{2}-14 x_{3}+x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.616 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=39 x_{1}+8 x_{2}-16 x_{3} \\ x_{2}^{\prime }=-36 x_{1}-5 x_{2}+16 x_{3} \\ x_{3}^{\prime }=72 x_{1}+16 x_{2}-29 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.908 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=28 x_{1}+50 x_{2}+100 x_{3} \\ x_{2}^{\prime }=15 x_{1}+33 x_{2}+60 x_{3} \\ x_{3}^{\prime }=-15 x_{1}-30 x_{2}-57 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.974 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+17 x_{2}+4 x_{3} \\ x_{2}^{\prime }=-x_{1}+6 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{2}+2 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.551 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \\ x_{3}^{\prime }=-3 x_{1}+2 x_{2}+x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.548 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+5 x_{2}-5 x_{3} \\ x_{2}^{\prime }=3 x_{1}-x_{2}+3 x_{3} \\ x_{3}^{\prime }=8 x_{1}-8 x_{2}+10 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.577 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-15 x_{1}-7 x_{2}+4 x_{3} \\ x_{2}^{\prime }=34 x_{1}+16 x_{2}-11 x_{3} \\ x_{3}^{\prime }=17 x_{1}+7 x_{2}+5 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.682 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{2}+x_{3}-2 x_{4} \\ x_{2}^{\prime }=7 x_{1}-4 x_{2}-6 x_{3}+11 x_{4} \\ x_{3}^{\prime }=5 x_{1}-x_{2}+x_{3}+3 x_{4} \\ x_{4}^{\prime }=6 x_{1}-2 x_{2}-2 x_{3}+6 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.176 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}-2 x_{3}+x_{4} \\ x_{2}^{\prime }=3 x_{2}-5 x_{3}+3 x_{4} \\ x_{3}^{\prime }=-13 x_{2}+22 x_{3}-12 x_{4} \\ x_{4}^{\prime }=-27 x_{2}+45 x_{3}-25 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.074 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=35 x_{1}-12 x_{2}+4 x_{3}+30 x_{4} \\ x_{2}^{\prime }=22 x_{1}-8 x_{2}+3 x_{3}+19 x_{4} \\ x_{3}^{\prime }=-10 x_{1}+3 x_{2}-9 x_{4} \\ x_{4}^{\prime }=-27 x_{1}+9 x_{2}-3 x_{3}-23 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.053 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=11 x_{1}-x_{2}+26 x_{3}+6 x_{4}-3 x_{5} \\ x_{2}^{\prime }=3 x_{2} \\ x_{3}^{\prime }=-9 x_{1}-24 x_{3}-6 x_{4}+3 x_{5} \\ x_{4}^{\prime }=3 x_{1}+9 x_{3}+5 x_{4}-x_{5} \\ x_{5}^{\prime }=-48 x_{1}-3 x_{2}-138 x_{3}-30 x_{4}+18 x_{5} \end {array}\right ] \] |
1 |
1 |
5 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.577 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2}+x_{3} \\ x_{2}^{\prime }=4 x_{1}+3 x_{2}+x_{4} \\ x_{3}^{\prime }=3 x_{3}-4 x_{4} \\ x_{4}^{\prime }=4 x_{3}+3 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.792 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-8 x_{3}-3 x_{4} \\ x_{2}^{\prime }=-18 x_{1}-x_{2} \\ x_{3}^{\prime }=-9 x_{1}-3 x_{2}-25 x_{3}-9 x_{4} \\ x_{4}^{\prime }=33 x_{1}+10 x_{2}+90 x_{3}+32 x_{4} \end {array}\right ] \] |
1 |
1 |
4 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.805 |
|
|
\[ {}y^{\prime } = y \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
0.459 |
|
|
\[ {}y^{\prime } = 4 y \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
0.543 |
|
|
\[ {}2 y^{\prime }+3 y = 0 \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
0.548 |
|
|
\[ {}2 x y+y^{\prime } = 0 \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.53 |
|
|
\[ {}y^{\prime } = x^{2} y \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.488 |
|
|
\[ {}\left (-2+x \right ) y^{\prime }+y = 0 \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.584 |
|
|
\[ {}\left (2 x -1\right ) y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.601 |
|
|
\[ {}2 \left (1+x \right ) y^{\prime } = y \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.608 |
|
|
\[ {}\left (-1+x \right ) y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.592 |
|
|
\[ {}2 \left (-1+x \right ) y^{\prime } = 3 y \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.584 |
|
|
\[ {}y^{\prime \prime } = y \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.494 |
|
|
\[ {}y^{\prime \prime } = 4 y \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.533 |
|
|
\[ {}y^{\prime \prime }+9 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.589 |
|
|
\[ {}y^{\prime \prime }+y = x \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.671 |
|
|
\[ {}x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
first order ode series method. Regular singular point |
[_separable] |
✓ |
✓ |
0.391 |
|
|
\[ {}2 x y^{\prime } = y \] |
1 |
1 |
1 |
first order ode series method. Regular singular point |
[_separable] |
✓ |
✓ |
0.404 |
|
|
\[ {}x^{2} y^{\prime }+y = 0 \] |
1 |
0 |
0 |
first order ode series method. Irregular singular point |
[_separable] |
❇ |
N/A |
0.326 |
|
|
\[ {}x^{3} y^{\prime } = 2 y \] |
1 |
0 |
0 |
first order ode series method. Irregular singular point |
[_separable] |
❇ |
N/A |
0.263 |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.132 |
|
|
\[ {}y^{\prime \prime }-4 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.742 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.858 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.863 |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Complex roots |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.774 |
|
|
\[ {}y^{\prime } = 1+y^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.427 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.105 |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.939 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.802 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.922 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.594 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer] |
✓ |
✓ |
1.015 |
|
|
\[ {}\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.964 |
|
|
\[ {}\left (-x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+16 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.809 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer] |
✓ |
✓ |
1.147 |
|
|
\[ {}3 y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.676 |
|
|
\[ {}5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.157 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.052 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.918 |
|
|
\[ {}y^{\prime \prime }+x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.62 |
|
|
\[ {}y^{\prime \prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.658 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.212 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.279 |
|
|
\[ {}y^{\prime \prime }+\left (-1+x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.931 |
|
|
\[ {}\left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (-1+x \right ) y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.664 |
|
|
\[ {}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.833 |
|
|
\[ {}\left (4 x^{2}+16 x +17\right ) y^{\prime \prime } = 8 y \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.982 |
|
|
\[ {}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.364 |
|
|
\[ {}y^{\prime \prime }+\left (1+x \right ) y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.891 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }+2 x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.466 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.107 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.071 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}+1\right ) y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.634 |
|
|
\[ {}y^{\prime \prime }+{\mathrm e}^{-x} y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.036 |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.58 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } \sin \left (x \right )+x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Lienard] |
✓ |
✓ |
5.636 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+2 \alpha y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.105 |
|
|
\[ {}y^{\prime \prime } = x y \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.616 |
|
|
|
|||||||||
|
|
|||||||||