| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }&=3 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.241 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.895 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -8 y&={\mathrm e}^{x} \left (x^{2}+2\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
22.982 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
30.631 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }-8 y&={\mathrm e}^{x} \left (x^{2}+2\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
36.000 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+4 y&={\mathrm e}^{2 x} \cos \left (x \right )+{\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
35.172 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&={\mathrm e}^{2 x} \left (x +3\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
35.357 |
|
| \begin{align*}
y^{\prime \prime }+y&=x +2 \,{\mathrm e}^{-x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| \begin{align*}
y^{\prime \prime }-y&=x \,{\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
55.079 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
36.946 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.154 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
30.723 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
31.007 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.274 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| \begin{align*}
y^{\prime \prime }-3 y&=x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
9.938 |
|
| \begin{align*}
4 y^{\prime \prime }+7 y^{\prime }+3 y&=5 \cos \left (t \right ) \\
y \left (0\right ) &= -3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.736 |
|
| \begin{align*}
e i u^{\prime \prime \prime \prime }&=\cos \left (x \right ) \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| \begin{align*}
e i u^{\prime \prime \prime \prime }&={\mathrm e}^{-x} \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.137 |
|
| \begin{align*}
e i u^{\prime \prime \prime \prime }&=\sinh \left (x \right ) \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.307 |
|
| \begin{align*}
e i u^{\prime \prime \prime \prime }&=1 \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.132 |
|
| \begin{align*}
e i u^{\prime \prime \prime \prime }&=x^{2} \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.155 |
|
| \begin{align*}
e i u^{\prime \prime \prime \prime }&=x^{4} \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.164 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{a x} \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= y_{1} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
55.750 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (a x \right ) \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= y_{1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.013 |
|
| \begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.142 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
26.989 |
|
| \begin{align*}
y^{\prime \prime }+10 y^{\prime }+25 y&=\frac {{\mathrm e}^{-5 x} \ln \left (x \right )}{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
27.560 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 x}}{x^{3}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
31.973 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right ) \csc \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \begin{align*}
y^{\prime \prime }-12 y^{\prime }+36 y&={\mathrm e}^{6 x} \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
22.849 |
|
| \begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
26.583 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x^{4}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
27.175 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{-x} \ln \left (x \right )}{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
31.199 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
27.033 |
|
| \begin{align*}
5 x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=\sqrt {x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.835 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=x^{{1}/{4}} \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.397 |
|
| \begin{align*}
-3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=\frac {1}{x^{3}} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.860 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+7 y^{\prime } x -3 y&=\frac {\ln \left (x \right )}{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.411 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\ln \left (x \right ) \left (\frac {1}{x^{3}}+\frac {1}{x^{5}}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
17.079 |
|
| \begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
15.711 |
|
| \begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.147 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\
y \left (1\right ) &= {\mathrm e} \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
17.318 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 x}}{x^{3}} \\
y \left (1\right ) &= 4 \,{\mathrm e}^{-3} \\
y^{\prime }\left (1\right ) &= -2 \,{\mathrm e}^{-3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
24.988 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x^{4}} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= {\mathrm e}^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
19.886 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= {\frac {5}{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
63.298 |
|
| \begin{align*}
-3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=\frac {1}{x^{3}} \\
y \left (\frac {1}{4}\right ) &= 0 \\
y^{\prime }\left (\frac {1}{4}\right ) &= {\frac {14}{9}} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.074 |
|
| \begin{align*}
2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=\left (x^{2}+1\right )^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.350 |
|
| \begin{align*}
y^{\left (5\right )}-y^{\prime }-\frac {4 y}{x}&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✓ |
0.046 |
|
| \begin{align*}
x \left (1-2 x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+4 x^{2} \ln \left (x \right )\right ) y^{\prime }-\left (2+4 x \right ) y&={\mathrm e}^{2 x} \left (1-2 x \ln \left (x \right )\right )^{2} \\
y \left (\frac {1}{2}\right ) &= \frac {{\mathrm e}}{2} \\
y^{\prime }\left (\frac {1}{2}\right ) &= {\mathrm e} \left (2+\ln \left (2\right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
✗ |
1.151 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=-\frac {{\mathrm e}^{-t}}{\left (1+t \right )^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
28.159 |
|
| \begin{align*}
x_{1}^{\prime }&=2 x_{1}+x_{2} \\
x_{2}^{\prime }&=-3 x_{1}+6 x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.476 |
|
| \begin{align*}
x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\
x_{2}^{\prime }&=-2 x_{1}+3 x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.505 |
|
| \begin{align*}
x_{1}^{\prime }&=2 \sin \left (t \right ) x_{1}+\ln \left (t \right ) x_{2} \\
x_{2}^{\prime }&=\frac {x_{1}}{-2+t}+\frac {{\mathrm e}^{t} x_{2}}{1+t} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (3\right ) &= 0 \\
x_{2} \left (3\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✗ |
✓ |
0.049 |
|
| \begin{align*}
x^{\prime }&=5 x-6 y+1 \\
y^{\prime }&=6 x-7 y+1 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| \begin{align*}
x^{\prime }&=5 x-6 y \\
y^{\prime }&=6 x-7 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.455 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| \begin{align*}
x^{\prime }&=y-z \\
y^{\prime }&=z-x \\
z^{\prime }&=x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.878 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+\left (1-t \right ) x_{2} \\
x_{2}^{\prime }&=\frac {x_{1}}{t}-x_{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.037 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{2}-x_{3}+x_{4} \\
x_{2}^{\prime }&=-x_{2}+x_{4} \\
x_{3}^{\prime }&=x_{3}-x_{4} \\
x_{4}^{\prime }&=2 x_{4} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.038 |
|
| \begin{align*}
x_{1}^{\prime }&=5 x_{1}+2 x_{2}+2 x_{3} \\
x_{2}^{\prime }&=2 x_{1}+2 x_{2}-4 x_{3} \\
x_{3}^{\prime }&=2 x_{1}-4 x_{2}+2 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 2 \\
x_{2} \left (0\right ) &= 1 \\
x_{3} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| \begin{align*}
x_{1}^{\prime }&=-10 x_{1}+x_{2}+7 x_{3} \\
x_{2}^{\prime }&=-9 x_{1}+4 x_{2}+5 x_{3} \\
x_{3}^{\prime }&=-17 x_{1}+x_{2}+12 x_{3} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 5 \\
x_{2} \left (0\right ) &= 2 \\
x_{3} \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.863 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.442 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=x_{1} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2}+3 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}+2 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1 \\
x_{2}^{\prime }&=x_{1}+t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
x^{\prime }&=5 x-6 y+1 \\
y^{\prime }&=6 x-7 y+1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| \begin{align*}
t x^{\prime }&=3 x-2 y \\
y^{\prime } t&=x+y-t^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.038 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y+2 t^{2} \\
y^{\prime }&=5 x+y-1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.256 |
|
| \begin{align*}
x_{1}^{\prime }&=x_{1}+2 x_{2} \\
x_{2}^{\prime }&=4 x_{1}+x_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
N_{1}^{\prime }&=4 N_{1}-6 N_{2} \\
N_{2}^{\prime }&=8 N_{1}-10 N_{2} \\
\end{align*} With initial conditions \begin{align*}
N_{1} \left (0\right ) &= 100000 \\
N_{2} \left (0\right ) &= 1000 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.518 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2} \\
x_{2}^{\prime }&=2 x_{1}+x_{2} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= 1 \\
x_{2} \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2} \\
x_{2}^{\prime }&=x_{1} \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -1 \\
x_{2} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
x_{1}^{\prime }&=4 x_{1}-x_{2}+3 \,{\mathrm e}^{2 t} \\
x_{2}^{\prime }&=2 x_{1}+x_{2}+2 t \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -{\frac {5}{18}} \\
x_{2} \left (0\right ) &= {\frac {47}{9}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.693 |
|
| \begin{align*}
x_{1}^{\prime }&=3 x_{1}-2 x_{2}+1 \\
x_{2}^{\prime }&=x_{1}+t \\
\end{align*} With initial conditions \begin{align*}
x_{1} \left (0\right ) &= -{\frac {1}{2}} \\
x_{2} \left (0\right ) &= -{\frac {1}{4}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| \begin{align*}
x^{\prime }&=5 x-6 y+1 \\
y^{\prime }&=6 x-7 y+1 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \begin{align*}
t x^{\prime }&=3 x-2 y \\
y^{\prime } t&=x+y-t^{2} \\
\end{align*} With initial conditions \begin{align*}
x \left (1\right ) &= 1 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.037 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y+2 t^{2} \\
y^{\prime }&=5 x+y-1 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= {\frac {534}{2197}} \\
y \left (0\right ) &= {\frac {567}{2197}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.848 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=4 x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.255 |
|
| \begin{align*}
x^{\prime }&=-2 x+y \\
y^{\prime }&=x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \begin{align*}
x^{\prime }&=3 x-2 y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.429 |
|
| \begin{align*}
x^{\prime }&=-x \\
y^{\prime }&=-x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \begin{align*}
x^{\prime }&=-x+y \\
y^{\prime }&=-x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
x^{\prime }&=2 x-y \\
y^{\prime }&=9 x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.498 |
|
| \begin{align*}
x^{\prime }&=2 x+y \\
y^{\prime }&=-3 x+6 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=z \\
z^{\prime }&=x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
2.694 |
|
| \begin{align*}
c_{1}^{\prime }&=-\frac {k c_{1}}{V_{1}}+\frac {k c_{2}}{V_{1}} \\
c_{2}^{\prime }&=\frac {k c_{1}}{V_{2}}-\frac {k c_{2}}{V_{2}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \begin{align*}
x^{\prime }&=a \left (b -x\right )-c f y \\
y^{\prime }&=d \left (x-y\right )-c f y-a y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= b \\
y \left (0\right ) &= \frac {d b}{a +d} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.151 |
|
| \begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=-3 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.415 |
|