|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime \prime }+9 y = 18 \,{\mathrm e}^{3 x} \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.52 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.37 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = x^{2} \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.44 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \sin \left (x \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.49 |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 0 \] |
higher_order_laplace |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.504 |
|
|
\[ {}y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.227 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.85 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (-1+x \right )^{2} & 1\le x \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.462 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.473 |
|
|
\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.03 |
|
|
\[ {}y^{\prime \prime }-4 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.082 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.207 |
|
|
\[ {}y^{\prime }+3 y = \delta \left (-2+x \right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.819 |
|
|
\[ {}y^{\prime }-3 y = \delta \left (-1+x \right )+2 \operatorname {Heaviside}\left (-2+x \right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.398 |
|
|
\[ {}y^{\prime \prime }+9 y = \delta \left (x -\pi \right )+\delta \left (x -3 \pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.817 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \delta \left (-1+x \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.796 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = \cos \left (x \right )+2 \delta \left (x -\pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.654 |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (x \right ) \delta \left (x -\pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.614 |
|
|
\[ {}y^{\prime \prime }+a^{2} y = \delta \left (x -\pi \right ) f \left (x \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.027 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.328 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}-2 y_{2} \\ y_{2}^{\prime }=y_{1}+3 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.47 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2}+x -1 \\ y_{2}^{\prime }=3 y_{1}+2 y_{2}-5 x -2 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.6 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=\frac {2 y_{1}}{x}-\frac {y_{2}}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}} \\ y_{2}^{\prime }=2 y_{1}+1-6 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.026 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\ y_{2}^{\prime }=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.029 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}-2 y_{2} \\ y_{2}^{\prime }=-y_{1}+y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.642 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\ y_{2}^{\prime }=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
❇ |
N/A |
0.028 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\ y_{2}^{\prime }=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
❇ |
N/A |
0.026 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }={\mathrm e}^{-x} y_{1}-\sqrt {1+x}\, y_{2}+x^{2} \\ y_{2}^{\prime }=\frac {y_{1}}{\left (-2+x \right )^{2}} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
❇ |
N/A |
0.027 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }={\mathrm e}^{-x} y_{1}-\sqrt {1+x}\, y_{2}+x^{2} \\ y_{2}^{\prime }=\frac {y_{1}}{\left (-2+x \right )^{2}} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
❇ |
N/A |
0.03 |
|
|
\(\left [\begin {array}{cc} -2 & -4 \\ 1 & 3 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.125 |
|
|
\(\left [\begin {array}{cc} -3 & -1 \\ 2 & -1 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.175 |
|
|
\(\left [\begin {array}{ccc} 1 & 0 & 1 \\ 0 & 1 & -1 \\ -2 & 0 & -1 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.257 |
|
|
\(\left [\begin {array}{ccc} 3 & 1 & -1 \\ 1 & 3 & -1 \\ 3 & 3 & -1 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.166 |
|
|
\(\left [\begin {array}{ccc} 7 & -1 & 6 \\ -10 & 4 & -12 \\ -2 & 1 & -1 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.223 |
|
|
\(\left [\begin {array}{cccc} 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.199 |
|
|
\(\left [\begin {array}{cccc} 1 & 3 & 5 & 7 \\ 2 & 6 & 10 & 14 \\ 3 & 9 & 15 & 21 \\ 6 & 18 & 30 & 42 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.243 |
|
|
\(\left [\begin {array}{ccccc} 1 & 3 & 5 & 2 & 4 \\ 5 & 2 & 4 & 1 & 3 \\ 4 & 1 & 3 & 5 & 2 \\ 3 & 5 & 2 & 4 & 1 \\ 2 & 4 & 1 & 3 & 5 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
6.331 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2}+5 \,{\mathrm e}^{x} \\ y_{2}^{\prime }=y_{1}+4 y_{2}-2 \,{\mathrm e}^{-x} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.425 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{2}-2 y_{1}+\sin \left (2 x \right ) \\ y_{2}^{\prime }=-3 y_{1}+y_{2}-2 \cos \left (3 x \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
6.501 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{2} \\ y_{2}^{\prime }=3 y_{1} \\ y_{3}^{\prime }=2 y_{3}-y_{1} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.733 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 x y_{1}-x^{2} y_{2}+4 x \\ y_{2}^{\prime }={\mathrm e}^{x} y_{1}+3 \,{\mathrm e}^{-x} y_{2}-\cos \left (3 x \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
❇ |
N/A |
0.03 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.307 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2}+4 x -2 \\ y_{2}^{\prime }=y_{1}-2 y_{2}+3 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.758 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x} \\ y_{2}^{\prime }=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.025 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\ y_{2}^{\prime }=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.026 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}+y_{2}-2 y_{3} \\ y_{2}^{\prime }=3 y_{2}-2 y_{3} \\ y_{3}^{\prime }=3 y_{1}+y_{2}-3 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.497 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-5 y_{2}-5 y_{3} \\ y_{2}^{\prime }=-y_{1}+4 y_{2}+2 y_{3} \\ y_{3}^{\prime }=3 y_{1}-5 y_{2}-3 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.776 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}+6 y_{2}+6 y_{3} \\ y_{2}^{\prime }=y_{1}+3 y_{2}+2 y_{3} \\ y_{3}^{\prime }=-y_{1}-4 y_{2}-3 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.554 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2}-3 y_{3} \\ y_{2}^{\prime }=-3 y_{1}+4 y_{2}-2 y_{3} \\ y_{3}^{\prime }=2 y_{1}+y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.921 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}-y_{2}+y_{3} \\ y_{2}^{\prime }=-y_{1}-2 y_{2}-y_{3} \\ y_{3}^{\prime }=y_{1}-y_{2}-2 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.466 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+y_{2}+2 y_{3} \\ y_{2}^{\prime }=y_{1}+y_{2}+2 y_{3} \\ y_{3}^{\prime }=2 y_{1}+2 y_{2}+4 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.419 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}+y_{2} \\ y_{2}^{\prime }=-y_{1}+2 y_{2} \\ y_{3}^{\prime }=3 y_{3}-4 y_{4} \\ y_{4}^{\prime }=4 y_{3}+3 y_{4} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.944 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=-3 y_{1}+2 y_{3} \\ y_{3}^{\prime }=y_{4} \\ y_{4}^{\prime }=2 y_{1}-5 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
4.61 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+2 y_{2} \\ y_{2}^{\prime }=-2 y_{1}+3 y_{2} \\ y_{3}^{\prime }=y_{3} \\ y_{4}^{\prime }=2 y_{4} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.71 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{2}+y_{4} \\ y_{2}^{\prime }=y_{1}-y_{3} \\ y_{3}^{\prime }=y_{4} \\ y_{4}^{\prime }=y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.611 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=-x+2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.319 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=-2 x+3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.344 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=2 x-3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.873 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=5 x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.493 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=-2 x-y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.454 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=2 x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.426 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-5 x-y+2 \\ y^{\prime }=3 x-y-3 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.754 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x-2 y-6 \\ y^{\prime }=4 x-y+2 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.625 |
|
|
\[ {}y^{\prime } = \frac {y+1}{t +1} \] |
exact, linear, separable, homogeneousTypeD2, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.167 |
|
|
\[ {}y^{\prime } = t^{2} y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.587 |
|
|
\[ {}y^{\prime } = t^{4} y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.699 |
|
|
\[ {}y^{\prime } = 2 y+1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.259 |
|
|
\[ {}y^{\prime } = 2-y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.244 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{-y} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.154 |
|
|
\[ {}x^{\prime } = 1+x^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.223 |
|
|
\[ {}y^{\prime } = 2 t y^{2}+3 y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.711 |
|
|
\[ {}y^{\prime } = \frac {t}{y} \] |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.332 |
|
|
\[ {}y^{\prime } = \frac {t}{t^{2} y+y} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.818 |
|
|
\[ {}y^{\prime } = t y^{\frac {1}{3}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.068 |
|
|
\[ {}y^{\prime } = \frac {1}{2 y+1} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.36 |
|
|
\[ {}y^{\prime } = \frac {2 y+1}{t} \] |
exact, linear, separable, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.311 |
|
|
\[ {}y^{\prime } = y \left (1-y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.509 |
|
|
\[ {}y^{\prime } = \frac {4 t}{1+3 y^{2}} \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
154.546 |
|
|
\[ {}v^{\prime } = t^{2} v-2-2 v+t^{2} \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.914 |
|
|
\[ {}y^{\prime } = \frac {1}{t y+t +y+1} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.904 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{t} y}{1+y^{2}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.037 |
|
|
\[ {}y^{\prime } = y^{2}-4 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.503 |
|
|
\[ {}w^{\prime } = \frac {w}{t} \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.747 |
|
|
\[ {}y^{\prime } = \sec \left (y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.297 |
|
|
\[ {}x^{\prime } = -x t \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.188 |
|
|
\[ {}y^{\prime } = t y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.984 |
|
|
\[ {}y^{\prime } = -y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.24 |
|
|
\[ {}y^{\prime } = t^{2} y^{3} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.401 |
|
|
\[ {}y^{\prime } = -y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.194 |
|
|
\[ {}y^{\prime } = \frac {t}{y-t^{2} y} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.08 |
|
|
\[ {}y^{\prime } = 2 y+1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.46 |
|
|
\[ {}y^{\prime } = t y^{2}+2 y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.93 |
|
|
\[ {}x^{\prime } = \frac {t^{2}}{x+t^{3} x} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.807 |
|
|
\[ {}y^{\prime } = \frac {1-y^{2}}{y} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.778 |
|
|
\[ {}y^{\prime } = \left (1+y^{2}\right ) t \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.343 |
|
|
\[ {}y^{\prime } = \frac {1}{2 y+3} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.266 |
|
|
\[ {}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.02 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+5}{y} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.503 |
|
|
\[ {}y^{\prime } = t^{2}+t \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.134 |
|
|
\[ {}y^{\prime } = t^{2}+1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.157 |
|
|
|
||||||
|
|
||||||