| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.161 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+6 y^{\prime } x +6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.521 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +58 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.189 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+25 y^{\prime } x +144 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.180 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-11 y^{\prime } x +35 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.014 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x -21 y&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.576 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x&=0 \\
y \left (2\right ) &= 5 \\
y^{\prime }\left (2\right ) &= 8 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
y \left (1\right ) &= 4 \\
y^{\prime }\left (1\right ) &= 5 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.355 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+25 y^{\prime } x +144 y&=0 \\
y \left (1\right ) &= -4 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.297 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-9 y^{\prime } x +24 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 10 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.122 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
y \left (1\right ) &= 7 \\
y^{\prime }\left (1\right ) &= -3 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.935 |
|
| \begin{align*}
y^{\prime }+4 y&=1 \\
y \left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \begin{align*}
y^{\prime }-9 y&=t \\
y \left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| \begin{align*}
y^{\prime }+4 y&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \begin{align*}
y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| \begin{align*}
-2 y+y^{\prime }&=1-t \\
y \left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| \begin{align*}
y^{\prime \prime }+y&=1 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=t^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=1+t \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <4 \\ 3 & 4\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.225 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=\left \{\begin {array}{cc} 0 & 0\le t <4 \\ 12 & 4\le t \end {array}\right . \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.194 |
|
| \begin{align*}
y^{\prime \prime \prime }-8 y&=\left \{\begin {array}{cc} 0 & 0\le t <6 \\ 2 & 6\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
10.731 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} -2 & 0\le t <3 \\ 0 & 3\le 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]] |
✓ |
✓ |
✓ |
✗ |
4.916 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=\left \{\begin {array}{cc} 1 & 0\le t <5 \\ 2 & 5\le t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
10.318 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t <3 \\ t +2 & 3\le t \end {array}\right . \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
6.082 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.395 |
|
| \begin{align*}
y^{\prime \prime }+10 y^{\prime }+24 y&=f \left (t \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.517 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+12 y&=f \left (t \right ) \\
y \left (0\right ) &= -3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.824 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }-5 y&=f \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.458 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=f \left (t \right ) \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.176 |
|
| \begin{align*}
y^{\prime \prime }-k^{2} y&=f \left (t \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.625 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-11 y^{\prime \prime }+18 y&=f \left (t \right ) \\
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]] |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=3 \delta \left (-2+t \right )-4 \delta \left (t -5\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.746 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=4 \delta \left (t -3\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.000 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+2 y&=6 \delta \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| \begin{align*}
y^{\prime \prime }+16 y^{\prime }&=12 \delta \left (t -\frac {5 \pi }{8}\right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.142 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=8 \delta \left (t \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \begin{align*}
x^{\prime }-2 y^{\prime }&=1 \\
x^{\prime }-x+y&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| \begin{align*}
2 x^{\prime }-3 y+y^{\prime }&=0 \\
x^{\prime }+y^{\prime }&=t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.622 |
|
| \begin{align*}
x^{\prime }+2 y^{\prime }-y&=1 \\
2 x^{\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 |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
x^{\prime }+y^{\prime }-x&=\cos \left (t \right ) \\
x^{\prime }+2 y^{\prime }&=0 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
3 x^{\prime }-y&=2 t \\
x^{\prime }+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 |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| \begin{align*}
x^{\prime }+4 y^{\prime }-y&=0 \\
x^{\prime }+2 y&={\mathrm e}^{-t} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.621 |
|
| \begin{align*}
x^{\prime }+2 x-y^{\prime }&=0 \\
x^{\prime }+x+y&=t^{2} \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.608 |
|
| \begin{align*}
x^{\prime }+4 x-y&=0 \\
x^{\prime }+y^{\prime }&=t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| \begin{align*}
x^{\prime }+y^{\prime }+x-y&=0 \\
x^{\prime }+2 y^{\prime }+x&=1 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| \begin{align*}
x^{\prime }-x+2 y^{\prime }&=0 \\
4 x^{\prime }+3 y^{\prime }+y&=-6 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
y_{1}^{\prime }-2 y_{2}^{\prime }+3 y_{1}&=0 \\
y_{1}-4 y_{2}^{\prime }+3 y_{3}&=t \\
y_{1}-2 y_{2}^{\prime }+3 y_{3}^{\prime }&=-1 \\
\end{align*}
With initial conditions \begin{align*}
y_{1} \left (0\right ) &= 0 \\
y_{2} \left (0\right ) &= 0 \\
y_{3} \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.889 |
|
| \begin{align*}
t^{2} y^{\prime }-2 y&=2 \\
\end{align*}
Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
35.572 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime } t -4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -7 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.741 |
|
| \begin{align*}
y^{\prime \prime }-16 y^{\prime } t +32 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.692 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime } t -8 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.746 |
|
| \begin{align*}
t y^{\prime \prime }+\left (t -1\right ) y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.567 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime } t -4 y&=6 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[_erf] |
✓ |
✓ |
✓ |
✗ |
0.783 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime } t&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime } t +4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 10 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.774 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime } t +16 y&=3 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.806 |
|
| \begin{align*}
\left (1-t \right ) y^{\prime \prime }+y^{\prime } t -y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| \begin{align*}
y^{\prime }-y x&=1-x \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
y^{\prime }-x^{3} y&=4 \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.603 |
|
| \begin{align*}
y^{\prime }+\left (-x^{2}+1\right ) y&=x \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.897 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x +y&=3 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.816 |
|
| \begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }+2 y&=x \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.918 |
|
| \begin{align*}
y^{\prime \prime }+y x&=\cos \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.720 |
|
| \begin{align*}
y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y&=-x^{2}+1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.962 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x&=1-{\mathrm e}^{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.732 |
|
| \begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
1.309 |
|
| \begin{align*}
y^{\prime \prime } x -2 y^{\prime } x +2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.784 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-9\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.240 |
|
| \begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.401 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x -y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.087 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.158 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.908 |
|
| \begin{align*}
\left (-x +2\right ) x y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.280 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.227 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right ) \\
y \left (1\right ) &= \frac {\pi }{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.170 |
|
| \begin{align*}
y^{\prime }&=x \cos \left (2 x \right )-y \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.571 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right ) y-3 x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
3.546 |
|
| \begin{align*}
y^{\prime }&=-y+{\mathrm e}^{x} \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.086 |
|
| \begin{align*}
y^{\prime }-\cos \left (x \right ) y&=-x^{2}+1 \\
y \left (2\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.094 |
|
| \begin{align*}
y^{\prime }&=3+2 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.553 |
|
| \(\left [\begin {array}{cc} 1 & 3 \\ 2 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.484 |
|
| \(\left [\begin {array}{cc} -2 & 0 \\ 1 & 4 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.428 |
|
| \(\left [\begin {array}{cc} -5 & 0 \\ 1 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.386 |
|
| \(\left [\begin {array}{cc} 6 & -2 \\ -3 & 4 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.537 |
|
| \(\left [\begin {array}{cc} 1 & -6 \\ 2 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.550 |
|
| \(\left [\begin {array}{cc} 0 & 1 \\ 0 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.261 |
|
| \(\left [\begin {array}{ccc} 2 & 0 & 0 \\ 1 & 0 & 2 \\ 0 & 0 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.608 |
|
| \(\left [\begin {array}{ccc} -2 & 1 & 0 \\ 1 & 3 & 0 \\ 0 & 0 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.875 |
|
| \(\left [\begin {array}{ccc} -3 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 1 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.471 |
|
| \(\left [\begin {array}{ccc} 0 & 0 & -1 \\ 0 & 0 & 1 \\ 2 & 0 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.816 |
|
| \(\left [\begin {array}{ccc} -14 & 1 & 0 \\ 0 & 2 & 0 \\ 1 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.510 |
|
| \(\left [\begin {array}{ccc} 3 & 0 & 0 \\ 1 & -2 & -8 \\ 0 & -5 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.754 |
|
| \(\left [\begin {array}{ccc} 1 & -2 & 0 \\ 0 & 0 & 0 \\ -5 & 0 & 7 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.702 |
|