| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| \begin{align*}
y^{\prime \prime }-y&=\frac {1}{\sqrt {1-{\mathrm e}^{2 x}}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
63.333 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{-2 x} \sin \left ({\mathrm e}^{-x}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
66.635 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=15 \,{\mathrm e}^{-x} \sqrt {x +1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
27.388 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=2 \tan \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
63.951 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
76.780 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\frac {1}{{\mathrm e}^{x}+1} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
6.096 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.142 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=\frac {5 \ln \left (x \right )}{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
45.085 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=9 x^{2} \ln \left (x \right ) \\
\end{align*} |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
\left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
33.360 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=60 \cos \left (3 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=9 \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -6 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.238 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=2 t^{2}+1 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.265 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=8 \sin \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=4 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{t} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.261 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=8 \sin \left (t \right ) {\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=8 \,{\mathrm e}^{t} \sin \left (2 t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=54 t \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.281 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.081 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=2 \sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=8 \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.982 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.810 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{t} \operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.163 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=\delta \left (-2+t \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.337 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=4 \operatorname {Heaviside}\left (t -\pi \right )+2 \delta \left (t -\pi \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=10 \,{\mathrm e}^{-t} \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= -2 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=120 \,{\mathrm e}^{3 t} \operatorname {Heaviside}\left (t -1\right ) \\
y \left (0\right ) &= 15 \\
y^{\prime }\left (0\right ) &= -6 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.946 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y&=40 \operatorname {Heaviside}\left (-2+t \right ) t^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.669 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y&=\left (2 t^{2}+t +1\right ) \delta \left (t -1\right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.204 |
|
| \begin{align*}
x^{\prime }+2 x-y&=0 \\
x+y^{\prime }-2 y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
2 x^{\prime }+x-5 y^{\prime }-4 y&=0 \\
-y^{\prime }-2 x+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
x^{\prime }-x+3 y&=0 \\
3 x-y^{\prime }+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=0 \\
x^{\prime }+x-y^{\prime }&=0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.052 |
|
| \begin{align*}
x^{\prime \prime }-3 x-4 y&=0 \\
x+y^{\prime \prime }+y&=0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.038 |
|
| \begin{align*}
y_{1}^{\prime }-y_{2}&=0 \\
4 y_{1}+y_{2}^{\prime }-4 y_{2}-2 y_{3}&=0 \\
-2 y_{1}+y_{2}+y_{3}^{\prime }+y_{3}&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \begin{align*}
y_{1}^{\prime }-2 y_{1}+3 y_{2}-3 y_{3}&=0 \\
-4 y_{1}+y_{2}^{\prime }+5 y_{2}-3 y_{3}&=0 \\
-4 y_{1}+4 y_{2}+y_{3}^{\prime }-2 y_{3}&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.731 |
|
| \begin{align*}
x^{\prime }+x+2 y&=8 \\
2 x+y^{\prime }-2 y&=2 \,{\mathrm e}^{-t}-8 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| \begin{align*}
x^{\prime }&=2 x-3 y+t \,{\mathrm e}^{-t} \\
y^{\prime }&=2 x-3 y+{\mathrm e}^{-t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.660 |
|
| \begin{align*}
x^{\prime }-x-2 y&={\mathrm e}^{t} \\
-4 x+y^{\prime }-3 y&=1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.927 |
|
| \begin{align*}
x^{\prime }-4 x+3 y&=\sin \left (t \right ) \\
-2 x+y^{\prime }+y&=-2 \cos \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.831 |
|
| \begin{align*}
x^{\prime }-y&=0 \\
-x+y^{\prime }&={\mathrm e}^{t}+{\mathrm e}^{-t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| \begin{align*}
x^{\prime }+2 x+5 y&=0 \\
-x+y^{\prime }-2 y&=\sin \left (2 t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.831 |
|
| \begin{align*}
x^{\prime }-2 x+2 y^{\prime }&=-4 \,{\mathrm e}^{2 t} \\
2 x^{\prime }-3 x+3 y^{\prime }-y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.705 |
|
| \begin{align*}
3 x^{\prime }+2 x+y^{\prime }-6 y&=5 \,{\mathrm e}^{t} \\
4 x^{\prime }+2 x+y^{\prime }-8 y&=5 \,{\mathrm e}^{t}+2 t -3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| \begin{align*}
x^{\prime }-5 x+3 y&=2 \,{\mathrm e}^{3 t} \\
-x+y^{\prime }-y&=5 \,{\mathrm e}^{-t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.381 |
|
| \begin{align*}
x^{\prime }-2 x+y&=0 \\
x+y^{\prime }-2 y&=-5 \,{\mathrm e}^{t} \sin \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.797 |
|
| \begin{align*}
x^{\prime }+4 x+2 y&=\frac {2}{{\mathrm e}^{t}-1} \\
6 x-y^{\prime }+3 y&=\frac {3}{{\mathrm e}^{t}-1} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.043 |
|
| \begin{align*}
x^{\prime }-x+y&=\sec \left (t \right ) \\
-2 x+y^{\prime }+y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.899 |
|
| \begin{align*}
x^{\prime }-x-2 y&=16 \,{\mathrm e}^{t} t \\
2 x-y^{\prime }-2 y&=0 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.314 |
|
| \begin{align*}
x^{\prime }-2 x+y&=5 \,{\mathrm e}^{t} \cos \left (t \right ) \\
x+y^{\prime }-2 y&=10 \,{\mathrm e}^{t} \sin \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.324 |
|
| \begin{align*}
x^{\prime }-4 x+3 y&=\sin \left (t \right ) \\
2 x+y^{\prime }-y&=2 \cos \left (t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= x_{0} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \begin{align*}
x^{\prime }-2 x-y&=2 \,{\mathrm e}^{t} \\
x-y^{\prime }+2 y&=3 \,{\mathrm e}^{4 t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= x_{0} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.297 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y&=40 \,{\mathrm e}^{3 t} \\
x^{\prime }+x-y^{\prime }&=36 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 3 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.031 |
|
| \begin{align*}
x^{\prime }-2 x-y&=2 \,{\mathrm e}^{t} \\
y^{\prime }-2 y-4 z&=4 \,{\mathrm e}^{2 t} \\
x-z^{\prime }-z&=0 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 9 \\
y \left (0\right ) &= 3 \\
z \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| \begin{align*}
x^{\prime \prime }+2 x-2 y^{\prime }&=0 \\
3 x^{\prime }+y^{\prime \prime }-8 y&=240 \,{\mathrm e}^{t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.037 |
|
| \begin{align*}
x^{\prime }-x-2 y&=0 \\
x-y^{\prime }&=15 \cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= x_{0} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
x^{\prime }-x+y&=2 \sin \left (t \right ) \left (1-\operatorname {Heaviside}\left (t -\pi \right )\right ) \\
2 x-y^{\prime }-y&=0 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| \begin{align*}
2 x^{\prime }+x-5 y^{\prime }-4 y&=28 \,{\mathrm e}^{t} \operatorname {Heaviside}\left (-2+t \right ) \\
3 x^{\prime }-2 x-4 y^{\prime }+y&=0 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2} \\
x_{2}^{\prime }&=-4 x_{1}+x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-3 x_{2} \\
x_{2}^{\prime }&=3 x_{1}+x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}+3 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}-x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+2 x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{1}-x_{2}+2 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}+x_{3} \\
x_{3}^{\prime }&=4 x_{1}-x_{2}+4 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.889 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2} \\
x_{2}^{\prime }&=x_{1}+3 x_{2}-x_{3} \\
x_{3}^{\prime }&=-x_{1}+2 x_{2}+3 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.095 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}-x_{3} \\
x_{2}^{\prime }&=3 x_{1}-4 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-4 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}-x_{3} \\
x_{3}^{\prime }&=-2 x_{2}+2 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= -2 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+x_{2}-2 x_{3} \\
x_{2}^{\prime }&=4 x_{1}+x_{2} \\
x_{3}^{\prime }&=2 x_{1}+x_{2}-x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.748 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}+26 \sin \left (t \right ) \\
x_{2}^{\prime }&=3 x_{1}+4 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.912 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+8 x_{2}+9 t \\
x_{2}^{\prime }&=x_{1}+x_{2}+3 \,{\mathrm e}^{-t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.525 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}+2 x_{2} \\
x_{2}^{\prime }&=-3 x_{1}+4 x_{2}+\frac {{\mathrm e}^{3 t}}{1+{\mathrm e}^{2 t}} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.051 |
|
| \begin{align*}
x_{1}^{\prime }&=-4 x_{1}-2 x_{2}+\frac {2}{{\mathrm e}^{t}-1} \\
x_{2}^{\prime }&=6 x_{1}+3 x_{2}-\frac {3}{{\mathrm e}^{t}-1} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.046 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=-2 x_{1}+3 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| \begin{align*}
x_{1}^{\prime }&=-x_{1}-5 x_{2} \\
x_{2}^{\prime }&=x_{1}+x_{2}+\frac {4}{\sin \left (2 t \right )} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.180 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2}+27 t \\
x_{2}^{\prime }&=-x_{1}+4 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.617 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-x_{2}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=4 x_{1}-x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=2 x_{1}-x_{2}+35 \,{\mathrm e}^{t} t^{{3}/{2}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}+x_{3} \\
x_{2}^{\prime }&=x_{1}+x_{2}-x_{3}+6 \,{\mathrm e}^{-t} \\
x_{3}^{\prime }&=2 x_{1}-x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.194 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-2 x_{2}-x_{3} \\
x_{2}^{\prime }&=-x_{1}+x_{2}+x_{3}+12 t \\
x_{3}^{\prime }&=x_{1}-x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.190 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2}-2 x_{3}+{\mathrm e}^{t} \\
x_{2}^{\prime }&=x_{1}+x_{2} \\
x_{3}^{\prime }&=6 x_{1}-6 x_{2}+5 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
546.063 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}-x_{2}-x_{3}+4 \,{\mathrm e}^{t} \\
x_{2}^{\prime }&=x_{1}+x_{2} \\
x_{3}^{\prime }&=3 x_{1}+x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.431 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}+2 x_{3} \\
x_{2}^{\prime }&=x_{1}+2 x_{3} \\
x_{3}^{\prime }&=-2 x_{1}+x_{2}-x_{3}+4 \sin \left (t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.642 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2}-x_{3}+{\mathrm e}^{3 t} \\
x_{2}^{\prime }&=x_{1}+2 x_{2}-x_{3} \\
x_{3}^{\prime }&=x_{1}+x_{2}+2 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
3.378 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{2}-x_{3}+2 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=3 x_{1}-2 x_{2}-3 x_{3} \\
x_{3}^{\prime }&=-x_{1}+x_{2}+2 x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}-x_{3}+24 t \\
x_{2}^{\prime }&=x_{1}-x_{2} \\
x_{3}^{\prime }&=3 x_{1}-x_{2}-x_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.985 |
|
| \begin{align*}
y^{\prime \prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.341 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.292 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \begin{align*}
y^{\prime \prime }-2 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| \begin{align*}
y^{\prime \prime }-2 x^{2} y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+\left (4 x -1\right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
y^{\prime \prime }+\left (\cos \left (x \right )+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \begin{align*}
y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+k y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
0.975 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (-2 x^{2}+x \right ) y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.660 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (\frac {1}{2} x +x^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.842 |
|