| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
2 x -2 \,{\mathrm e}^{y x} \sin \left (2 x \right )+{\mathrm e}^{y x} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{y x} x \cos \left (2 x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
4.510 |
|
| \begin{align*}
\frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.004 |
|
| \begin{align*}
x \ln \left (x \right )+y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
7.579 |
|
| \begin{align*}
\frac {x}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (y^{2}+x^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.998 |
|
| \begin{align*}
2 x -y+\left (-x +2 y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.322 |
|
| \begin{align*}
-1+9 x^{2}+y+\left (x -4 y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.816 |
|
| \begin{align*}
x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.812 |
|
| \begin{align*}
y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
1.602 |
|
| \begin{align*}
\left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.371 |
|
| \begin{align*}
2 y x +3 x^{2} y+y^{3}+\left (y^{2}+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
✓ |
✓ |
✗ |
2.355 |
|
| \begin{align*}
y^{\prime }&=-1+{\mathrm e}^{2 x}+y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.780 |
|
| \begin{align*}
1+\left (-\sin \left (y\right )+\frac {x}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
1.779 |
|
| \begin{align*}
y+\left (-{\mathrm e}^{-2 y}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.379 |
|
| \begin{align*}
{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.815 |
|
| \begin{align*}
\frac {4 x^{3}}{y^{2}}+\frac {3}{y}+\left (\frac {3 x}{y^{2}}+4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
1.767 |
|
| \begin{align*}
3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime }&=0 \\
\end{align*} | [_rational] | ✓ | ✓ | ✓ | ✗ | 1.818 |
|
| \begin{align*}
3 y x +y^{2}+\left (x^{2}+y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
4.971 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}-2 y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.092 |
|
| \begin{align*}
y^{\prime }&=\frac {\cos \left (x \right )+1}{2-\sin \left (y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.103 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y}{3-x +3 y^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.059 |
|
| \begin{align*}
y^{\prime }&=3-6 x +y-2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.744 |
|
| \begin{align*}
y^{\prime }&=\frac {-1-2 y x -y^{2}}{x^{2}+2 y x} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
1.990 |
|
| \begin{align*}
y x +y^{\prime } x&=1-y \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.897 |
|
| \begin{align*}
y^{\prime }&=\frac {4 x^{3}+1}{y \left (2+3 y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
1.562 |
|
| \begin{align*}
y^{\prime } x +2 y&=\frac {\sin \left (x \right )}{x} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.704 |
|
| \begin{align*}
y^{\prime }&=\frac {-1-2 y x}{x^{2}+2 y} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
1.381 |
|
| \begin{align*}
\frac {-x^{2}+x +1}{x^{2}}+\frac {y y^{\prime }}{y-2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.451 |
|
| \begin{align*}
x^{2}+y+\left ({\mathrm e}^{y}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
1.658 |
|
| \begin{align*}
y^{\prime }+y&=\frac {1}{{\mathrm e}^{x}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.606 |
|
| \begin{align*}
y^{\prime }&=1+2 x +y^{2}+2 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.346 |
|
| \begin{align*}
x +y+\left (x +2 y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.979 |
|
| \begin{align*}
\left ({\mathrm e}^{x}+1\right ) y^{\prime }&=y-{\mathrm e}^{x} y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.868 |
|
| \begin{align*}
y^{\prime }&=\frac {-{\mathrm e}^{2 y} \cos \left (x \right )+\cos \left (y\right ) {\mathrm e}^{-x}}{2 \,{\mathrm e}^{2 y} \sin \left (x \right )-\sin \left (y\right ) {\mathrm e}^{-x}} \\
\end{align*} |
[NONE] |
✓ |
✓ |
✓ |
✗ |
32.668 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 x}+3 y \\
\end{align*} | [[_linear, ‘class A‘]] | ✓ | ✓ | ✓ | ✓ | 1.065 |
|
| \begin{align*}
2 y+y^{\prime }&={\mathrm e}^{-x^{2}-2 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.530 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{2}-2 y-y^{3}}{2 x +3 x y^{2}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
1.885 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{x +y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.374 |
|
| \begin{align*}
\frac {-4+6 y x +2 y^{2}}{3 x^{2}+4 y x +3 y^{2}}+y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
1.938 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-1}{1+y^{2}} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.893 |
|
| \begin{align*}
\left (t +1\right ) y+t y^{\prime }&={\mathrm e}^{2 t} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.702 |
|
| \begin{align*}
2 \cos \left (x \right ) \sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.643 |
|
| \begin{align*}
\frac {2 x}{y}-\frac {y}{y^{2}+x^{2}}+\left (-\frac {x^{2}}{y^{2}}+\frac {x}{y^{2}+x^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.289 |
|
| \begin{align*}
y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.560 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{x^{2}+y^{3}+y} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| \begin{align*}
3 t +2 y&=-t y^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.783 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.743 |
|
| \begin{align*}
2 y x +3 y^{2}-\left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
5.053 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 y x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
4.156 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| \begin{align*}
6 y^{\prime \prime }-y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.202 |
|
| \begin{align*}
2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.194 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.819 |
|
| \begin{align*}
4 y^{\prime \prime }-9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.988 |
|
| \begin{align*}
y^{\prime \prime }-9 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.237 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.228 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.343 |
|
| \begin{align*}
6 y^{\prime \prime }-5 y^{\prime }+y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.996 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+3 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
2 y^{\prime \prime }+y^{\prime }-4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.373 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }-9 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
4 y^{\prime \prime }-y&=0 \\
y \left (-2\right ) &= 1 \\
y^{\prime }\left (-2\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.177 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= {\frac {5}{4}} \\
y^{\prime }\left (0\right ) &= -{\frac {3}{4}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.099 |
|
| \begin{align*}
2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=0 \\
y \left (0\right ) &= \alpha \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
4 y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= \beta \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.750 |
|
| \begin{align*}
y^{\prime \prime }-\left (2 \alpha -1\right ) y^{\prime }+\alpha \left (\alpha -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.233 |
|
| \begin{align*}
y^{\prime \prime }+\left (3-\alpha \right ) y^{\prime }-2 \left (\alpha -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.292 |
|
| \begin{align*}
2 y^{\prime \prime }+3 y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -\beta \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✗ | 0.277 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= \beta \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.286 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.292 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.298 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-8 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.224 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.301 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.241 |
|
| \begin{align*}
4 y^{\prime \prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.246 |
|
| \begin{align*}
9 y^{\prime \prime }+9 y^{\prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.207 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.239 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.259 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.690 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (\frac {\pi }{3}\right ) &= 2 \\
y^{\prime }\left (\frac {\pi }{3}\right ) &= -4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.309 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.354 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
y \left (\frac {\pi }{4}\right ) &= 2 \\
y^{\prime }\left (\frac {\pi }{4}\right ) &= -2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
u^{\prime \prime }-u^{\prime }+2 u&=0 \\
u \left (0\right ) &= 2 \\
u^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
5 u^{\prime \prime }+2 u^{\prime }+7 u&=0 \\
u \left (0\right ) &= 2 \\
u^{\prime }\left (0\right ) &= 1 \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.458 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+6 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= \alpha \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.384 |
|
| \begin{align*}
y^{\prime \prime }+2 a y^{\prime }+\left (a^{2}+1\right ) y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+t y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+4 t y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.262 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }+\frac {5 y}{4}&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.029 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.865 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| \begin{align*}
t^{2} y^{\prime \prime }-t y^{\prime }+5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+3 t y^{\prime }-3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| \begin{align*}
t^{2} y^{\prime \prime }+7 t y^{\prime }+10 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.940 |
|