| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
43.913 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+6 x y^{\prime }+6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
33.243 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 x y^{\prime }+58 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
25.498 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+25 x y^{\prime }+144 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.222 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-11 x y^{\prime }+35 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
33.829 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 x y^{\prime }-21 y&=0 \\
y \left (2\right ) &= 1 \\
y^{\prime }\left (2\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.135 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }&=0 \\
y \left (2\right ) &= 5 \\
y^{\prime }\left (2\right ) &= 8 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+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)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.459 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+25 x y^{\prime }+144 y&=0 \\
y \left (1\right ) &= -4 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.418 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-9 x y^{\prime }+24 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 10 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.335 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-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)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.116 |
|
| \begin{align*}
y^{\prime }+4 y&=1 \\
y \left (0\right ) &= -3 \\
\end{align*}
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| \begin{align*}
y^{\prime }-9 y&=t \\
y \left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \begin{align*}
y^{\prime }+4 y&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
y^{\prime }+2 y&={\mathrm e}^{-t} \\
y \left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.241 |
|
| \begin{align*}
-2 y+y^{\prime }&=1-t \\
y \left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.188 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.245 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.209 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=t +1 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.225 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.202 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
17.555 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.416 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
16.367 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.645 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.664 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.505 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.077 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=3 \delta \left (t -2\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]] |
✓ |
✓ |
✓ |
✓ |
1.331 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=4 \delta \left (-3+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.745 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.225 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.175 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.266 |
|
| \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 |
✓ |
✓ |
✓ |
✗ |
1.444 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.224 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.184 |
|
| \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 |
✓ |
✓ |
✓ |
✗ |
0.168 |
|
| \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 |
✓ |
✓ |
✓ |
✗ |
0.175 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.160 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.167 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| \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 |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
t^{2} y^{\prime }-2 y&=2 \\
\end{align*}
Using Laplace transform method. |
[_separable] |
✓ |
✓ |
✓ |
✓ |
24.920 |
|
| \begin{align*}
y^{\prime \prime }+4 t y^{\prime }-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]] |
✓ |
✓ |
✓ |
✗ |
0.273 |
|
| \begin{align*}
y^{\prime \prime }-16 t y^{\prime }+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]] |
✓ |
✓ |
✓ |
✗ |
0.201 |
|
| \begin{align*}
y^{\prime \prime }+8 t y^{\prime }-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]] |
✓ |
✓ |
✓ |
✗ |
0.224 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.165 |
|
| \begin{align*}
y^{\prime \prime }+2 t y^{\prime }-4 y&=6 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[_erf] |
✓ |
✓ |
✓ |
✗ |
0.242 |
|
| \begin{align*}
y^{\prime \prime }+8 t y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.224 |
|
| \begin{align*}
y^{\prime \prime }-4 t y^{\prime }+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]] |
✓ |
✓ |
✓ |
✗ |
0.228 |
|
| \begin{align*}
y^{\prime \prime }-8 t y^{\prime }+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]] |
✓ |
✓ |
✓ |
✗ |
0.253 |
|
| \begin{align*}
\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.261 |
|
| \begin{align*}
y^{\prime }-y x&=1-x \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.422 |
|
| \begin{align*}
y^{\prime }-x^{3} y&=4 \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
y^{\prime }+\left (-x^{2}+1\right ) y&=x \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }+y&=3 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }+y x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }+2 y&=x \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.436 |
|
| \begin{align*}
y^{\prime \prime }+y x&=\cos \left (x \right ) \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.348 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.435 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }&=1-{\mathrm e}^{x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.392 |
|
| \begin{align*}
x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| \begin{align*}
x y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-9\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \begin{align*}
4 x y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.886 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 x y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }-\left (x^{2}-2\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| \begin{align*}
x y^{\prime \prime }-y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.317 |
|
| \begin{align*}
\left (2-x \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]] |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| \begin{align*}
y^{\prime }&=\sin \left (y\right ) \\
y \left (1\right ) &= \frac {\pi }{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
16.656 |
|
| \begin{align*}
y^{\prime }&=x \cos \left (2 x \right )-y \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.852 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (x \right )-3 x^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.597 |
|
| \begin{align*}
y^{\prime }&=-y+{\mathrm e}^{x} \\
y \left (-2\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.845 |
|
| \begin{align*}
y^{\prime }-\cos \left (x \right ) y&=-x^{2}+1 \\
y \left (2\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.865 |
|
| \begin{align*}
y^{\prime }&=3+2 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.647 |
|
| \(\left [\begin {array}{cc} 1 & 3 \\ 2 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.301 |
|
| \(\left [\begin {array}{cc} -2 & 0 \\ 1 & 4 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.258 |
|
| \(\left [\begin {array}{cc} -5 & 0 \\ 1 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.258 |
|
| \(\left [\begin {array}{cc} 6 & -2 \\ -3 & 4 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.335 |
|
| \(\left [\begin {array}{cc} 1 & -6 \\ 2 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.359 |
|
| \(\left [\begin {array}{cc} 0 & 1 \\ 0 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.134 |
|
| \(\left [\begin {array}{ccc} 2 & 0 & 0 \\ 1 & 0 & 2 \\ 0 & 0 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.499 |
|
| \(\left [\begin {array}{ccc} -2 & 1 & 0 \\ 1 & 3 & 0 \\ 0 & 0 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.600 |
|
| \(\left [\begin {array}{ccc} -3 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 1 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.375 |
|
| \(\left [\begin {array}{ccc} 0 & 0 & -1 \\ 0 & 0 & 1 \\ 2 & 0 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.597 |
|
| \(\left [\begin {array}{ccc} -14 & 1 & 0 \\ 0 & 2 & 0 \\ 1 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.368 |
|
| \(\left [\begin {array}{ccc} 3 & 0 & 0 \\ 1 & -2 & -8 \\ 0 & -5 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.566 |
|
| \(\left [\begin {array}{ccc} 1 & -2 & 0 \\ 0 & 0 & 0 \\ -5 & 0 & 7 \end {array}\right ]\) |
Eigenvectors |
✓ |
N/A |
N/A |
N/A |
0.561 |
|