| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+11 y^{\prime \prime }-14 y^{\prime }+10 y&=-{\mathrm e}^{x} \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.798 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y&=2 \,{\mathrm e}^{x} \left (x +1\right )+{\mathrm e}^{-2 x} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.192 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y&=\sinh \left (x \right ) \cos \left (x \right )-\cosh \left (x \right ) \sin \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.871 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+9 y^{\prime \prime }+7 y^{\prime }+2 y&={\mathrm e}^{-x} \left (30+24 x \right )-{\mathrm e}^{-2 x} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+7 y^{\prime \prime }-6 y^{\prime }+2 y&={\mathrm e}^{x} \left (12 x -2 \cos \left (x \right )+2 \sin \left (x \right )\right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.795 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&={\mathrm e}^{2 x} \left (10+3 x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.126 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-2 y&=-{\mathrm e}^{3 x} \left (17 x^{2}+67 x +9\right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.156 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (-3 x^{2}-4 x +5\right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.158 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=-2 \,{\mathrm e}^{-x} \left (6 x^{2}-18 x +7\right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \left (x +1\right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=-{\mathrm e}^{-x} \left (3 x^{2}-9 x +4\right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.190 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{-2 x} \left (\left (23-2 x \right ) \cos \left (x \right )+\left (8-9 x \right ) \sin \left (x \right )\right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.210 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{x} \left (\left (28+6 x \right ) \cos \left (2 x \right )+\left (11-12 x \right ) \sin \left (2 x \right )\right ) \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.270 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y&={\mathrm e}^{x} \left (\left (2+6 x \right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.135 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{x} \left (1-6 x \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 7 \\
y^{\prime \prime }\left (0\right ) &= 9 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=-{\mathrm e}^{-x} \left (4-8 x \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.184 |
|
| \begin{align*}
4 y^{\prime \prime \prime }-3 y^{\prime }-y&={\mathrm e}^{-\frac {x}{2}} \left (2-3 x \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 15 \\
y^{\prime \prime }\left (0\right ) &= -17 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.200 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-x} \left (20-12 x \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -4 \\
y^{\prime \prime }\left (0\right ) &= 7 \\
y^{\prime \prime \prime }\left (0\right ) &= -22 \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.204 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y&=30 \cos \left (x \right )-10 \sin \left (x \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -4 \\
y^{\prime \prime }\left (0\right ) &= 16 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+5 y^{\prime \prime }-2 y^{\prime }&=-2 \,{\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -1 \\
y^{\prime \prime \prime }\left (0\right ) &= -5 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.529 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=2 x \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.305 |
|
| \begin{align*}
4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 y^{\prime } x +2 y&=30 x^{2} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{2} \\
\end{align*} |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.304 |
|
| \begin{align*}
16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 y^{\prime } x +9 y&=96 x^{{5}/{2}} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.413 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 y^{\prime } x +24 y&=x^{4} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=12 x^{2} \\
\end{align*} |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=4 x \\
y \left (1\right ) &= 4 \\
y^{\prime }\left (1\right ) &= 4 \\
y^{\prime \prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y&=x^{3} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
y^{\prime \prime }\left (1\right ) &= 7 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+16 y^{\prime } x -16 y&=9 x^{4} \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
y^{\prime \prime }\left (1\right ) &= 5 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \left (x +1\right ) \\
y \left (-1\right ) &= -6 \\
y^{\prime }\left (-1\right ) &= {\frac {43}{6}} \\
y^{\prime \prime }\left (-1\right ) &= -{\frac {5}{2}} \\
\end{align*} |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=9 x^{2} \\
y \left (1\right ) &= -7 \\
y^{\prime }\left (1\right ) &= -11 \\
y^{\prime \prime }\left (1\right ) &= -5 \\
y^{\prime \prime \prime }\left (1\right ) &= 6 \\
\end{align*} |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \begin{align*}
4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-y^{\prime } x +y&=6 x \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 0 \\
y^{\prime \prime }\left (1\right ) &= 4 \\
y^{\prime \prime \prime }\left (1\right ) &= -{\frac {37}{4}} \\
\end{align*} |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 y^{\prime } x +6 y&=40 x^{3} \\
y \left (-1\right ) &= -1 \\
y^{\prime }\left (-1\right ) &= -7 \\
y^{\prime \prime }\left (-1\right ) &= -1 \\
y^{\prime \prime \prime }\left (-1\right ) &= -31 \\
\end{align*} |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=F \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=F \left (x \right ) \\
\end{align*} |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=F \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=F \left (x \right ) \\
\end{align*} |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.427 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+2 y_{2} \\
y_{2}^{\prime }&=2 y_{1}+y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \begin{align*}
y_{1}^{\prime }&=-\frac {5 y_{1}}{4}+\frac {3 y_{2}}{4} \\
y_{2}^{\prime }&=\frac {3 y_{1}}{4}-\frac {5 y_{2}}{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
y_{1}^{\prime }&=-\frac {4 y_{1}}{5}+\frac {3 y_{2}}{5} \\
y_{2}^{\prime }&=-\frac {2 y_{1}}{5}-\frac {11 y_{2}}{5} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}-4 y_{2} \\
y_{2}^{\prime }&=-y_{1}-y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}-4 y_{2} \\
y_{2}^{\prime }&=-y_{1}-y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{1}-3 y_{2} \\
y_{2}^{\prime }&=2 y_{1}-y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
y_{1}^{\prime }&=-6 y_{1}-3 y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.419 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\
y_{2}^{\prime }&=y_{1}-2 y_{2}-3 y_{3} \\
y_{3}^{\prime }&=-4 y_{1}+y_{2}-y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.830 |
|
| \begin{align*}
y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-8 y_{3} \\
y_{2}^{\prime }&=-4 y_{1}-4 y_{3} \\
y_{3}^{\prime }&=-8 y_{1}-4 y_{2}-6 y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}+5 y_{2}+8 y_{3} \\
y_{2}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\
y_{3}^{\prime }&=-y_{1}-y_{2}-y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}-y_{2}+2 y_{3} \\
y_{2}^{\prime }&=12 y_{1}-4 y_{2}+10 y_{3} \\
y_{3}^{\prime }&=-6 y_{1}+y_{2}-7 y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.863 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{1}-y_{2}-4 y_{3} \\
y_{2}^{\prime }&=4 y_{1}-3 y_{2}-2 y_{3} \\
y_{3}^{\prime }&=y_{1}-y_{2}-y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \begin{align*}
y_{1}^{\prime }&=-2 y_{1}+2 y_{2}-6 y_{3} \\
y_{2}^{\prime }&=2 y_{1}+6 y_{2}+2 y_{3} \\
y_{3}^{\prime }&=-2 y_{1}-2 y_{2}+2 y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}+2 y_{2}-2 y_{3} \\
y_{2}^{\prime }&=-2 y_{1}+7 y_{2}-2 y_{3} \\
y_{3}^{\prime }&=-10 y_{1}+10 y_{2}-5 y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.652 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}+y_{2}-y_{3} \\
y_{2}^{\prime }&=3 y_{1}+5 y_{2}+y_{3} \\
y_{3}^{\prime }&=-6 y_{1}+2 y_{2}+4 y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}+4 y_{2} \\
y_{2}^{\prime }&=-y_{1}+7 y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{2} \\
y_{2}^{\prime }&=y_{1}-2 y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \begin{align*}
y_{1}^{\prime }&=-7 y_{1}+4 y_{2} \\
y_{2}^{\prime }&=-y_{1}-11 y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.364 |
|
| \begin{align*}
y_{1}^{\prime }&=3 y_{1}+y_{2} \\
y_{2}^{\prime }&=-y_{1}+y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{1}+12 y_{2} \\
y_{2}^{\prime }&=-3 y_{1}-8 y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
y_{1}^{\prime }&=-10 y_{1}+9 y_{2} \\
y_{2}^{\prime }&=-4 y_{1}+2 y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.353 |
|
| \begin{align*}
y_{1}^{\prime }&=-13 y_{1}+16 y_{2} \\
y_{2}^{\prime }&=-9 y_{1}+11 y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{2}+y_{3} \\
y_{2}^{\prime }&=-4 y_{1}+6 y_{2}+y_{3} \\
y_{3}^{\prime }&=4 y_{2}+2 y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \begin{align*}
y_{1}^{\prime }&=\frac {y_{1}}{3}+\frac {y_{2}}{3}-y_{3} \\
y_{2}^{\prime }&=-\frac {4 y_{1}}{3}-\frac {4 y_{2}}{3}+y_{3} \\
y_{3}^{\prime }&=-\frac {2 y_{1}}{3}+\frac {y_{2}}{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}+y_{2}-y_{3} \\
y_{2}^{\prime }&=-2 y_{1}+2 y_{3} \\
y_{3}^{\prime }&=-y_{1}+3 y_{2}-y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{1}-2 y_{2}-2 y_{3} \\
y_{2}^{\prime }&=-2 y_{1}+3 y_{2}-y_{3} \\
y_{3}^{\prime }&=2 y_{1}-y_{2}+3 y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \begin{align*}
y_{1}^{\prime }&=6 y_{1}-5 y_{2}+3 y_{3} \\
y_{2}^{\prime }&=2 y_{1}-y_{2}+3 y_{3} \\
y_{3}^{\prime }&=2 y_{1}+y_{2}+y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.692 |
|
| \begin{align*}
y_{1}^{\prime }&=-11 y_{1}+8 y_{2} \\
y_{2}^{\prime }&=-2 y_{1}-3 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 6 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
y_{1}^{\prime }&=15 y_{1}-9 y_{2} \\
y_{2}^{\prime }&=16 y_{1}-9 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 5 \\
y_{2} \left (0\right ) &= 8 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
y_{1}^{\prime }&=-3 y_{1}-4 y_{2} \\
y_{2}^{\prime }&=y_{1}-7 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 2 \\
y_{2} \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
y_{1}^{\prime }&=-7 y_{1}+24 y_{2} \\
y_{2}^{\prime }&=-6 y_{1}+17 y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 3 \\
y_{2} \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
y_{1}^{\prime }&=-7 y_{1}+3 y_{2} \\
y_{2}^{\prime }&=-3 y_{1}-y_{2} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}+y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\
y_{3}^{\prime }&=-y_{1}-y_{2}-y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 6 \\
y_{2} \left (0\right ) &= 5 \\
y_{3} \left (0\right ) &= -7 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \begin{align*}
y_{1}^{\prime }&=-2 y_{1}+2 y_{2}+y_{3} \\
y_{2}^{\prime }&=-2 y_{1}+2 y_{2}+y_{3} \\
y_{3}^{\prime }&=-3 y_{1}+3 y_{2}+2 y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -6 \\
y_{2} \left (0\right ) &= -2 \\
y_{3} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| \begin{align*}
y_{1}^{\prime }&=-7 y_{1}-4 y_{2}+4 y_{3} \\
y_{2}^{\prime }&=y_{1}+y_{3} \\
y_{3}^{\prime }&=-9 y_{1}-5 y_{2}+6 y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -6 \\
y_{2} \left (0\right ) &= 9 \\
y_{3} \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.197 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}-4 y_{2}-y_{3} \\
y_{2}^{\prime }&=3 y_{1}+6 y_{2}+y_{3} \\
y_{3}^{\prime }&=-3 y_{1}-2 y_{2}+3 y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -2 \\
y_{2} \left (0\right ) &= 1 \\
y_{3} \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| \begin{align*}
y_{1}^{\prime }&=4 y_{1}-8 y_{2}-4 y_{3} \\
y_{2}^{\prime }&=-3 y_{1}-y_{2}-4 y_{3} \\
y_{3}^{\prime }&=y_{1}-y_{2}+9 y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= -4 \\
y_{2} \left (0\right ) &= 1 \\
y_{3} \left (0\right ) &= -3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.885 |
|
| \begin{align*}
y_{1}^{\prime }&=-5 y_{1}-y_{2}+11 y_{3} \\
y_{2}^{\prime }&=-7 y_{1}+y_{2}+13 y_{3} \\
y_{3}^{\prime }&=-4 y_{1}+8 y_{3} \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 2 \\
y_{3} \left (0\right ) &= 2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| \begin{align*}
y_{1}^{\prime }&=5 y_{1}-y_{2}+y_{3} \\
y_{2}^{\prime }&=-y_{1}+9 y_{2}-3 y_{3} \\
y_{3}^{\prime }&=-2 y_{1}+2 y_{2}+4 y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+10 y_{2}-12 y_{3} \\
y_{2}^{\prime }&=2 y_{1}+2 y_{2}+3 y_{3} \\
y_{3}^{\prime }&=2 y_{1}-y_{2}+6 y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
y_{1}^{\prime }&=-6 y_{1}-4 y_{2}-4 y_{3} \\
y_{2}^{\prime }&=2 y_{1}-y_{2}+y_{3} \\
y_{3}^{\prime }&=2 y_{1}+3 y_{2}+y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{2}-2 y_{3} \\
y_{2}^{\prime }&=-y_{1}+5 y_{2}-3 y_{3} \\
y_{3}^{\prime }&=y_{1}+y_{2}+y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.597 |
|
| \begin{align*}
y_{1}^{\prime }&=-2 y_{1}-12 y_{2}+10 y_{3} \\
y_{2}^{\prime }&=2 y_{1}-24 y_{2}+11 y_{3} \\
y_{3}^{\prime }&=2 y_{1}-24 y_{2}+8 y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}-12 y_{2}+8 y_{3} \\
y_{2}^{\prime }&=y_{1}-9 y_{2}+4 y_{3} \\
y_{3}^{\prime }&=y_{1}-6 y_{2}+y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| \begin{align*}
y_{1}^{\prime }&=-4 y_{1}-y_{3} \\
y_{2}^{\prime }&=-y_{1}-3 y_{2}-y_{3} \\
y_{3}^{\prime }&=y_{1}-2 y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
y_{1}^{\prime }&=-3 y_{1}-3 y_{2}+4 y_{3} \\
y_{2}^{\prime }&=4 y_{1}+5 y_{2}-8 y_{3} \\
y_{3}^{\prime }&=2 y_{1}+3 y_{2}-5 y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| \begin{align*}
y_{1}^{\prime }&=-3 y_{1}-y_{2} \\
y_{2}^{\prime }&=y_{1}-y_{2} \\
y_{3}^{\prime }&=-y_{1}-y_{2}-2 y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
y_{1}^{\prime }&=-y_{1}+2 y_{2} \\
y_{2}^{\prime }&=-5 y_{1}+5 y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
y_{1}^{\prime }&=-11 y_{1}+4 y_{2} \\
y_{2}^{\prime }&=-26 y_{1}+9 y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
y_{1}^{\prime }&=y_{1}+2 y_{2} \\
y_{2}^{\prime }&=-4 y_{1}+5 y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
y_{1}^{\prime }&=5 y_{1}-6 y_{2} \\
y_{2}^{\prime }&=3 y_{1}-y_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| \begin{align*}
y_{1}^{\prime }&=-3 y_{1}-3 y_{2}+y_{3} \\
y_{2}^{\prime }&=2 y_{2}+2 y_{3} \\
y_{3}^{\prime }&=5 y_{1}+y_{2}+y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
8.529 |
|
| \begin{align*}
y_{1}^{\prime }&=-3 y_{1}+3 y_{2}+y_{3} \\
y_{2}^{\prime }&=y_{1}-5 y_{2}-3 y_{3} \\
y_{3}^{\prime }&=-3 y_{1}+7 y_{2}+3 y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.009 |
|
| \begin{align*}
y_{1}^{\prime }&=2 y_{1}+y_{2}-y_{3} \\
y_{2}^{\prime }&=y_{2}+y_{3} \\
y_{3}^{\prime }&=y_{1}+y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| \begin{align*}
y_{1}^{\prime }&=-3 y_{1}+y_{2}-3 y_{3} \\
y_{2}^{\prime }&=4 y_{1}-y_{2}+2 y_{3} \\
y_{3}^{\prime }&=4 y_{1}-2 y_{2}+3 y_{3} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| \begin{align*}
y^{\prime }+\sin \left (t \right ) y&=0 \\
y \left (0\right ) &= {\frac {3}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
y^{\prime }+{\mathrm e}^{t^{2}} y&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
y^{\prime }-2 t y&=t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.207 |
|
| \begin{align*}
2 t y+y^{\prime }&=t \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.297 |
|
| \begin{align*}
y+y^{\prime }&=\frac {1}{t^{2}+1} \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.314 |
|
| \begin{align*}
y \cos \left (t \right )+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.586 |
|
| \begin{align*}
\sqrt {t}\, \sin \left (t \right ) y+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.562 |
|
| \begin{align*}
\frac {2 t y}{t^{2}+1}+y^{\prime }&=\frac {1}{t^{2}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.695 |
|