| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{x^{2}}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
1.813 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+\left (-2 x^{3}+5 x \right ) y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \begin{align*}
\left (-3 x^{3}+3 x^{2}\right ) y^{\prime \prime }-\left (5 x^{2}+4 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.739 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
2.023 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+8 x^{2} y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.647 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (-x^{4}+x \right ) y^{\prime }+3 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \begin{align*}
\left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=3\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.586 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{2+x}+y&=0 \\
\end{align*} Series expansion around \(x=-2\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| \begin{align*}
4 y^{\prime \prime }+\frac {\left (4 x -3\right ) y}{\left (x -1\right )^{2}}&=0 \\
\end{align*} Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
\left (x -3\right )^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }-3 y&=0 \\
\end{align*} Series expansion around \(x=3\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| \begin{align*}
x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+\left (4 x^{2}+5 x \right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.893 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+9 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
x^{2} \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } x +\left (4 x^{3}-4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.113 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x +\left (1-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (2 x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.913 |
|
| \begin{align*}
y^{\prime \prime } x +4 y^{\prime }+\frac {12 y}{\left (2+x \right )^{2}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.004 |
|
| \begin{align*}
y^{\prime \prime } x +4 y^{\prime }+\frac {12 y}{\left (2+x \right )^{2}}&=0 \\
\end{align*} Series expansion around \(x=-2\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.844 |
|
| \begin{align*}
\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=3\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.628 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +3 y&=0 \\
\end{align*} Series expansion around \(x=1\). |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.974 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.637 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
2.052 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x -4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.902 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=1-2 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \begin{align*}
x^{\prime }&=4 x-3 y \\
y^{\prime }&=6 x-7 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.419 |
|
| \begin{align*}
t x^{\prime }+2 x&=15 y \\
y^{\prime } t&=x \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=5 x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 7 \\
y \left (0\right ) &= -7 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| \begin{align*}
x^{\prime }&=5 x+4 y \\
y^{\prime }&=8 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 9 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
x^{\prime }&=4 x+2 y \\
y^{\prime }&=3 x-y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= -21 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=5 x-2 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 15 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=2 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
x^{\prime }&=2 y \\
y^{\prime }&=-2 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| \begin{align*}
x^{\prime }&=-2 y \\
y^{\prime }&=8 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
x^{\prime }&=4 x-13 y \\
y^{\prime }&=x \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \begin{align*}
x^{\prime }&=3 x+2 y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= a_{1} \\
y \left (0\right ) &= a_{2} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
x^{\prime }&=8 x+2 y-17 \\
y^{\prime }&=4 x+y-13 \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \begin{align*}
x^{\prime }&=8 x+2 y+7 \,{\mathrm e}^{2 t} \\
y^{\prime }&=4 x+y-7 \,{\mathrm e}^{2 t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= -1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \begin{align*}
x^{\prime }&=4 x+3 y-6 \,{\mathrm e}^{3 t} \\
y^{\prime }&=x+6 y+2 \,{\mathrm e}^{3 t} \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 4 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| \begin{align*}
x^{\prime }&=-y \\
y^{\prime }&=4 x+24 t \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \begin{align*}
x^{\prime }&=4 x-13 y \\
y^{\prime }&=x+19 \cos \left (4 t \right )-13 \sin \left (4 t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 13 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.773 |
|
| \begin{align*}
x^{\prime }&=4 x+3 y+5 \operatorname {Heaviside}\left (-2+t \right ) \\
y^{\prime }&=x+6 y+17 \operatorname {Heaviside}\left (-2+t \right ) \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.066 |
|
| \begin{align*}
x^{\prime }&=5 x+4 y \\
y^{\prime }&=8 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \begin{align*}
x^{\prime }&=2 x-5 y \\
y^{\prime }&=3 x-7 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
x^{\prime }&=2 x-5 y+4 \\
y^{\prime }&=3 x-7 y+5 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.437 |
|
| \begin{align*}
x^{\prime }&=3 x+y \\
y^{\prime }&=6 x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \begin{align*}
x^{\prime }&=x y-6 y \\
y^{\prime }&=x-y-5 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.034 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=2 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| \begin{align*}
y y^{\prime }+y^{4}&=\sin \left (x \right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
7.724 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+5 y^{\prime }+y&={\mathrm e}^{x} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.170 |
|
| \begin{align*}
{y^{\prime }}^{2}+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.223 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+y^{\prime } t +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.341 |
|
| \begin{align*}
x {y^{\prime \prime }}^{2}+2 y&=2 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.098 |
|
| \begin{align*}
x^{\prime \prime }+2 \sin \left (x\right )&=\sin \left (2 t \right ) \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
2.485 |
|
| \begin{align*}
2 x -1-y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
2 x -y-y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.671 |
|
| \begin{align*}
2 y+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.252 |
|
| \begin{align*}
y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.670 |
|
| \begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.044 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-12 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.269 |
|
| \begin{align*}
y^{\prime \prime }+9 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.276 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }-10 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| \begin{align*}
x^{\prime \prime }+x&=t \cos \left (t \right )-\cos \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \begin{align*}
y^{\prime \prime }-12 y^{\prime }+40 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.310 |
|
| \begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-12 y^{\prime } x +42 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.573 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 y^{\prime } t +5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.602 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.733 |
|
| \begin{align*}
3 y \left (t^{2}+y\right )+t \left (t^{2}+6 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
13.158 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 y}{x}-3 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.427 |
|
| \begin{align*}
y \cos \left (t \right )+\left (2 y+\sin \left (t \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.500 |
|
| \begin{align*}
\frac {y}{x}+\cos \left (y\right )+\left (\ln \left (x \right )-x \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
7.122 |
|
| \begin{align*}
y^{\prime }&=\left (x^{2}-1\right ) \left (x^{3}-3 x \right )^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \begin{align*}
y^{\prime }&=x \sin \left (x^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x \ln \left (x \right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| \begin{align*}
y^{\prime }&=x \ln \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.422 |
|
| \begin{align*}
y^{\prime }&=\frac {-2 x -10}{\left (2+x \right ) \left (x -4\right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
y^{\prime }&=\frac {-x^{2}+x}{\left (x +1\right ) \left (x^{2}+1\right )} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {x^{2}-16}}{x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
y^{\prime }&=\left (-x^{2}+4\right )^{{3}/{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}-16} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x \right ) \cot \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.002 |
|
| \begin{align*}
y^{\prime }&=\sin \left (x \right )^{3} \tan \left (x \right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.884 |
|
| \begin{align*}
2 y+y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.697 |
|
| \begin{align*}
y+y^{\prime }&=\sin \left (t \right ) \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.234 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-12 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
y^{\prime \prime }+9 y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.256 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.094 |
|
| \begin{align*}
-4 y^{\prime }+y^{\prime \prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.095 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-12 y^{\prime } t +42 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.711 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.867 |
|