|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 4 t^{2} \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2, linear_second_order_ode_solved_by_an_integrating_factor, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.562 |
|
|
\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t \] |
kovacic, second_order_euler_ode, exact linear second order ode, second_order_integrable_as_is, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.5 |
|
|
\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = {\mathrm e}^{2 t} t^{2} \] |
kovacic, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.213 |
|
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (-1+t \right ) {\mathrm e}^{-t} \] |
kovacic, second_order_change_of_variable_on_y_method_2, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.074 |
|
|
\[ {}u^{\prime \prime }+2 u = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.872 |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+2 u = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.484 |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (\frac {t}{4}\right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.565 |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (2 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.287 |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (6 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.457 |
|
|
\[ {}u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5} = \cos \left (t \right ) \] |
unknown |
[NONE] |
❇ |
N/A |
0.103 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.523 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.836 |
|
|
\[ {}y^{\prime \prime }+k^{2} x^{2} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.906 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.883 |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.98 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.959 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.736 |
|
|
\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }+2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.764 |
|
|
\[ {}\left (-x^{2}+3\right ) y^{\prime \prime }-3 x y^{\prime }-y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.93 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.961 |
|
|
\[ {}2 y^{\prime \prime }+x y^{\prime }+3 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.135 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.22 |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.2 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.167 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.384 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+\lambda y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.231 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.095 |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.167 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.152 |
|
|
\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.801 |
|
|
\[ {}y^{\prime \prime }+x^{2} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.064 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
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)]‘]] |
✓ |
✓ |
2.602 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.16 |
|
|
\[ {}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.104 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y \ln \left (x \right ) = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.661 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+\sin \left (x \right ) y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.214 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+6 x y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.216 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+6 x y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.325 |
|
|
\[ {}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.72 |
|
|
\[ {}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.005 |
|
|
\[ {}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.976 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+4 x y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.957 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+4 x y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.497 |
|
|
\[ {}x y^{\prime \prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.108 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\alpha ^{2} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.509 |
|
|
\[ {}y^{\prime }-y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
0.5 |
|
|
\[ {}y^{\prime }-x y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.516 |
|
|
\[ {}\left (1-x \right ) y^{\prime } = y \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.556 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\alpha \left (\alpha +1\right ) y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer] |
✓ |
✓ |
1.694 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{10}+\frac {3 x_{2}}{40} \\ x_{2}^{\prime }=\frac {x_{1}}{10}-\frac {x_{2}}{5} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.543 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.799 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.727 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.682 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=\frac {9 x_{1}}{5}-x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.857 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.785 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2} \\ x_{2}^{\prime }=-5 x_{1}-x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.781 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=3 x_{1}+2 x_{2}+x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.048 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{3} \\ x_{2}^{\prime }=x_{1}-x_{2} \\ x_{3}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.487 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.594 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }=-x_{1}-x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.626 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=\frac {3 x_{1}}{4}-2 x_{2} \\ x_{2}^{\prime }=x_{1}-\frac {5 x_{2}}{4} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.766 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {4 x_{1}}{5}+2 x_{2} \\ x_{2}^{\prime }=-x_{1}+\frac {6 x_{2}}{5} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.747 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{4}+x_{2} \\ x_{2}^{\prime }=-x_{1}-\frac {x_{2}}{4} \\ x_{3}^{\prime }=-\frac {x_{3}}{4} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.807 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{4}+x_{2} \\ x_{2}^{\prime }=-x_{1}-\frac {x_{2}}{4} \\ x_{3}^{\prime }=\frac {x_{3}}{10} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.834 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{2}-\frac {x_{2}}{8} \\ x_{2}^{\prime }=2 x_{1}-\frac {x_{2}}{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.736 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.556 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-2 x_{2} \\ x_{2}^{\prime }=8 x_{1}-4 x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.439 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {3 x_{1}}{2}+x_{2} \\ x_{2}^{\prime }=-\frac {x_{1}}{4}-\frac {x_{2}}{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.582 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=-\frac {5 x_{1}}{2}+2 x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.576 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-x_{2}+x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.964 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.734 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}-7 x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.536 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {5 x_{1}}{2}+\frac {3 x_{2}}{2} \\ x_{2}^{\prime }=-\frac {3 x_{1}}{2}+\frac {x_{2}}{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.546 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+\frac {3 x_{2}}{2} \\ x_{2}^{\prime }=-\frac {3 x_{1}}{2}-x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.545 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+9 x_{2} \\ x_{2}^{\prime }=-x_{1}-3 x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.361 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=-4 x_{1}+x_{2} \\ x_{3}^{\prime }=3 x_{1}+6 x_{2}+2 x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.74 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {5 x_{1}}{2}+x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}-\frac {5 x_{2}}{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2}-\frac {5 x_{3}}{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.677 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}+t \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.206 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.966 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\sin \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.969 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+{\mathrm e}^{-2 t} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.288 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-2 x_{2}+\frac {1}{t^{3}} \\ x_{2}^{\prime }=8 x_{1}-4 x_{2}-\frac {1}{t^{2}} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.799 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}+2 x_{2}+\frac {1}{t} \\ x_{2}^{\prime }=2 x_{1}-x_{2}+\frac {2}{t}+4 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.916 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }=4 x_{1}+x_{2}-{\mathrm e}^{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.182 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}-{\mathrm e}^{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.031 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {5 x_{1}}{4}+\frac {3 x_{2}}{4}+2 t \\ x_{2}^{\prime }=\frac {3 x_{1}}{4}-\frac {5 x_{2}}{4}+{\mathrm e}^{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.267 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+\sqrt {2}\, x_{2}+{\mathrm e}^{-t} \\ x_{2}^{\prime }=\sqrt {2}\, x_{1}-2 x_{2}-{\mathrm e}^{-t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.92 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\cos \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.759 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}+\csc \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\sec \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
4.553 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{2}-\frac {x_{2}}{8}+\frac {{\mathrm e}^{-\frac {t}{2}}}{2} \\ x_{2}^{\prime }=2 x_{1}-\frac {x_{2}}{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.471 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t} \\ x_{2}^{\prime }=x_{1}-2 x_{2}+3 t \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.834 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}-2 x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.564 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.542 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.51 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}-7 x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.547 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.707 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.613 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.756 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2} \\ x_{2}^{\prime }=-\frac {5 x_{2}}{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.495 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.529 |
|
|
|
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