| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \(\left [\begin {array}{ccc} 1 & 1 & -1 \\ 2 & 3 & -4 \\ 4 & 1 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.490 |
|
| \(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & -6 & 6 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.516 |
|
| \(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & 1 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.488 |
|
| \(\left [\begin {array}{ccc} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.458 |
|
| \(\left [\begin {array}{ccc} 1 & 3 & -6 \\ 0 & 2 & 2 \\ 0 & -1 & 5 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.486 |
|
| \(\left [\begin {array}{ccc} -5 & -12 & 6 \\ 1 & 5 & -1 \\ -7 & -10 & 8 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.498 |
|
| \(\left [\begin {array}{ccc} -2 & 5 & 5 \\ -1 & 4 & 5 \\ 3 & -3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.494 |
|
| \(\left [\begin {array}{ccc} -2 & 6 & -18 \\ 12 & -23 & 66 \\ 5 & -10 & 29 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.500 |
|
| \begin{align*}
x^{\prime }&=x+y-z \\
y^{\prime }&=2 x+3 y-4 z \\
z^{\prime }&=4 x+y-4 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| \begin{align*}
x^{\prime }&=x-y-z \\
y^{\prime }&=x+3 y+z \\
z^{\prime }&=-3 x-6 y+6 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| \begin{align*}
-y+y^{\prime }&={\mathrm e}^{3 t} \\
y \left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.186 |
|
| \begin{align*}
y+y^{\prime }&=2 \sin \left (t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-12 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.145 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=8 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.179 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.167 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=18 \,{\mathrm e}^{-t} \sin \left (3 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.249 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y&=t \,{\mathrm e}^{-2 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.193 |
|
| \begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=4 t \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+15 y&=9 \,{\mathrm e}^{2 t} t \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 10 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.200 |
|
| \begin{align*}
y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=20 \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -2 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.270 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=36 t \,{\mathrm e}^{4 t} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -6 \\
\end{align*} Using Laplace transform method. | [[_3rd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.247 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.028 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.342 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.275 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+8 y&=\left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.705 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right . \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right . \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| \begin{align*}
t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.185 |
|
| \begin{align*}
t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 t x^{\prime }-6 x&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.134 |
|
| \begin{align*}
\left (t^{3}-2 t^{2}\right ) x^{\prime \prime }-\left (t^{3}+2 t^{2}-6 t \right ) x^{\prime }+\left (3 t^{2}-6\right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.762 |
|
| \begin{align*}
t^{3} x^{\prime \prime \prime }-\left (t +3\right ) t^{2} x^{\prime \prime }+2 t \left (t +3\right ) x^{\prime }-2 \left (t +3\right ) x&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.046 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+3 t x^{\prime }+3 x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.267 |
|
| \begin{align*}
\left (2 t +1\right ) x^{\prime \prime }+t^{3} x^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
1.203 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.758 |
|
| \begin{align*}
t^{3} x^{\prime \prime }-\left (t^{3}+2 t^{2}-t \right ) x^{\prime }+\left (t^{2}+t -1\right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.585 |
|
| \begin{align*}
t^{3} x^{\prime \prime }+3 t^{2} x^{\prime }+x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.229 |
|
| \begin{align*}
\sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
2.581 |
|
| \begin{align*}
\frac {\left (t +1\right ) x^{\prime \prime }}{t}-\frac {x^{\prime }}{t^{2}}+\frac {x}{t^{3}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.538 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+t x^{\prime }+x&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.922 |
|
| \begin{align*}
\left (t^{4}+t^{2}\right ) x^{\prime \prime }+2 t^{3} x^{\prime }+3 x&=0 \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✗ | ✓ | ✓ | ✗ | 53.710 |
|
| \begin{align*}
x^{\prime \prime }-\tan \left (t \right ) x^{\prime }+x&=0 \\
\end{align*} |
[_Lienard] |
✗ |
✓ |
✓ |
✗ |
2.818 |
|
| \begin{align*}
f \left (t \right ) x^{\prime \prime }+x g \left (t \right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.398 |
|
| \begin{align*}
x^{\prime \prime }+\left (t +1\right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.134 |
|
| \begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.948 |
|
| \begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.960 |
|
| \begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y \left (L \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.967 |
|
| \begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (L \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.094 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+\frac {\lambda y}{x}&=0 \\
y \left (1\right ) &= 0 \\
y \left ({\mathrm e}^{\pi }\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.171 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+\frac {\lambda y}{x}&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left ({\mathrm e}^{\pi }\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.053 |
|
| \begin{align*}
2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1}&=0 \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.956 |
|
| \begin{align*}
-\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.477 |
|
| \begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=3 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
x^{\prime }&=3 x+2 y \\
y^{\prime }&=x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
x^{\prime }&=3 x+4 y \\
y^{\prime }&=3 x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \begin{align*}
x^{\prime }&=2 x+5 y \\
y^{\prime }&=x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.373 |
|
| \begin{align*}
x^{\prime }&=2 x-4 y \\
y^{\prime }&=2 x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=4 x+5 y \\
\end{align*} | system_of_ODEs | ✓ | ✓ | ✓ | ✓ | 0.535 |
|
| \begin{align*}
x^{\prime }&=x-y \\
y^{\prime }&=x+5 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \begin{align*}
x^{\prime }&=x+7 y \\
y^{\prime }&=3 x+5 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=3 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.373 |
|
| \begin{align*}
x^{\prime }&=a x+b y \\
y^{\prime }&=c x+d y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.878 |
|
| \begin{align*}
x^{\prime }&=4 x-4 y-x \left (x^{2}+y^{2}\right ) \\
y^{\prime }&=4 x+4 y-y \left (x^{2}+y^{2}\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.044 |
|
| \begin{align*}
x^{\prime }&=y+\frac {x \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \\
y^{\prime }&=-x+\frac {y \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.065 |
|
| \begin{align*}
x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
21.581 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
20.315 |
|
| \begin{align*}
x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
11.904 |
|
| \begin{align*}
x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
12.202 |
|
| \begin{align*}
x^{\prime \prime }+\left (1+x^{2}\right ) x^{\prime }+x^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
11.835 |
|
| \begin{align*}
x^{\prime }&=x-x^{2} \\
y^{\prime }&=2 y-y^{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✗ |
0.050 |
|
| \begin{align*}
x^{\prime }&=\sin \left (t \right )+\cos \left (t \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.271 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}-1} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.238 |
|
| \begin{align*}
u^{\prime }&=4 t \ln \left (t \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.311 |
|
| \begin{align*}
z^{\prime }&={\mathrm e}^{-2 x} x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.266 |
|
| \begin{align*}
T^{\prime }&={\mathrm e}^{-t} \sin \left (2 t \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
x^{\prime }&=\sec \left (t \right )^{2} \\
x \left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| \begin{align*}
y^{\prime }&=x -\frac {1}{3} x^{3} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
x^{\prime }&=2 \sin \left (t \right )^{2} \\
x \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\
\end{align*} | [_quadrature] | ✓ | ✓ | ✓ | ✓ | 0.403 |
|
| \begin{align*}
x V^{\prime }&=x^{2}+1 \\
V \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t}&={\mathrm e}^{-t} \\
x \left (0\right ) &= 3 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| \begin{align*}
x^{\prime }&=1-x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
x^{\prime }&=x \left (2-x\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| \begin{align*}
x^{\prime }&=\left (1+x\right ) \left (2-x\right ) \sin \left (x\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.146 |
|
| \begin{align*}
x^{\prime }&=-x \left (1-x\right ) \left (2-x\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.910 |
|
| \begin{align*}
x^{\prime }&=x^{2}-x^{4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| \begin{align*}
x^{\prime }&=t^{3} \left (1-x\right ) \\
x \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.108 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2}\right ) \tan \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.947 |
|
| \begin{align*}
x^{\prime }&=t^{2} x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.992 |
|
| \begin{align*}
x^{\prime }&=-x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.356 |
|
| \begin{align*}
y^{\prime }&=y^{2} {\mathrm e}^{-t^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.701 |
|
| \begin{align*}
x^{\prime }+p x&=q \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \begin{align*}
y^{\prime } x&=k y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.506 |
|
| \begin{align*}
i^{\prime }&=p \left (t \right ) i \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.113 |
|
| \begin{align*}
x^{\prime }&=\lambda x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.816 |
|
| \begin{align*}
m v^{\prime }&=-m g +k v^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| \begin{align*}
x^{\prime }&=k x-x^{2} \\
x \left (0\right ) &= x_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.151 |
|
| \begin{align*}
x^{\prime }&=-x \left (k^{2}+x^{2}\right ) \\
x \left (0\right ) &= x_{0} \\
\end{align*} | [_quadrature] | ✓ | ✗ | ✓ | ✗ | 68.906 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.416 |
|
| \begin{align*}
x^{\prime }+t x&=4 t \\
x \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.120 |
|
| \begin{align*}
z^{\prime }&=z \tan \left (y \right )+\sin \left (y \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.935 |
|