| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{\prime \prime }-2 y&=\sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.600 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }-3 y&=-\frac {16 \ln \left (x \right )}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.625 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y&=x^{2}-2 x +2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.034 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=x^{m} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.974 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=2 \ln \left (x \right )^{2}+12 x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
31.922 |
|
| \begin{align*}
\left (x +1\right )^{3} y^{\prime \prime }+3 \left (x +1\right )^{2} y^{\prime }+\left (x +1\right ) y&=6 \ln \left (x +1\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
15.056 |
|
| \begin{align*}
\left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.263 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.063 |
|
| \begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
1.648 |
|
| \begin{align*}
\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (x +1\right ) y^{\prime }+6 y&=6 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.065 |
|
| \begin{align*}
x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.211 |
|
| \begin{align*}
y^{\prime \prime }+\left (\tan \left (x \right )-2 \cot \left (x \right )\right ) y^{\prime }+2 \cot \left (x \right )^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.263 |
|
| \begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.858 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y&=1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.351 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }-3 y&=5 x^{4} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=\left (x -1\right )^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.367 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-2 x}&={\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.451 |
|
| \begin{align*}
\left (x^{4}-x^{3}\right ) y^{\prime \prime }+\left (2 x^{3}-2 x^{2}-x \right ) y^{\prime }-y&=\frac {\left (x -1\right )^{2}}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.387 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }+y \,{\mathrm e}^{2 x}&=x \,{\mathrm e}^{2 x}-1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.099 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y&=x^{2} \left (2 x -3\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.379 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {1}{\sin \left (x \right )} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.692 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=\frac {1}{1+{\mathrm e}^{x}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.783 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {1}{\cos \left (x \right )^{3}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
8.131 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{2}+1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.770 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\frac {{\mathrm e}^{-x}}{\sin \left (x \right )} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.281 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {2}{\sin \left (x \right )^{3}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&={\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.001 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }&=\frac {x -1}{x^{3}} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.310 |
|
| \begin{align*}
x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }&=4 x^{3} {\mathrm e}^{x^{2}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.899 |
|
| \begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.250 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime \prime }-y^{\prime }&=\ln \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.299 |
|
| \begin{align*}
x y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }&=-4 x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.167 |
|
| \begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }&=\cos \left (x \right ) \cot \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.194 |
|
| \begin{align*}
4 x y^{\prime \prime }+2 y^{\prime }+y&=1 \\
y \left (\infty \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
22.739 |
|
| \begin{align*}
4 x y^{\prime \prime }+2 y^{\prime }+y&=\frac {6+x}{x^{2}} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
✗ |
509.012 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }&=\frac {1}{x^{2}+1} \\
y \left (\infty \right ) &= \frac {\pi ^{2}}{8} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✓ |
1.813 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=\left (x -1\right )^{2} {\mathrm e}^{x} \\
y \left (-\infty \right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
3.297 |
|
| \begin{align*}
2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y&=\frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
✗ |
73.719 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y&=4 \,{\mathrm e}^{x} \\
y \left (-\infty \right ) &= 0 \\
y^{\prime }\left (-1\right ) &= -{\mathrm e}^{-1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
✗ |
4.184 |
|
| \begin{align*}
x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x^{2} y^{\prime }+y x&=2 \ln \left (x \right ) \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
143.861 |
|
| \begin{align*}
\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-2 \left (1-x \right ) y&=2 x -2 \\
y \left (\infty \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
104.433 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+6 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.486 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| \begin{align*}
x^{\prime \prime }+{x^{\prime }}^{2}+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.589 |
|
| \begin{align*}
x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
152.345 |
|
| \begin{align*}
x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
2.250 |
|
| \begin{align*}
x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
127.523 |
|
| \begin{align*}
x^{\prime \prime }+x {x^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.953 |
|
| \begin{align*}
x^{\prime \prime }+\left (x+2\right ) x^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
3.592 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }+x-x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
123.835 |
|
| \begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
6.038 |
|
| \begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.970 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y \left (2 \pi \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.484 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (2 \pi \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
29.577 |
|
| \begin{align*}
1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
2.838 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= \alpha \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.017 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.397 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= {\mathrm e}^{\pi } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
y^{\prime \prime }+\alpha y^{\prime }&=0 \\
y \left (0\right ) &= {\mathrm e}^{\alpha } \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.089 |
|
| \begin{align*}
y^{\prime \prime }+\alpha ^{2} y&=1 \\
y^{\prime }\left (0\right ) &= \alpha \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
✓ |
30.609 |
|
| \begin{align*}
y^{\prime \prime }+y&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.589 |
|
| \begin{align*}
y^{\prime \prime }+\lambda ^{2} y&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.718 |
|
| \begin{align*}
y^{\prime \prime }+\lambda ^{2} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.977 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\
y \left (0\right ) &= -1 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.142 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-\lambda ^{4} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y \left (\pi \right ) &= 0 \\
y^{\prime \prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.159 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.576 |
|
| \begin{align*}
2 y^{\prime \prime }+4 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.254 |
|
| \begin{align*}
6 x y^{\prime \prime }+6 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.522 |
|
| \begin{align*}
y^{\prime }&=-y x +1 \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.573 |
|
| \begin{align*}
y^{\prime }&=\frac {-x +y}{x +y} \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
✓ |
0.398 |
|
| \begin{align*}
y^{\prime }&=y \sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \begin{align*}
y^{\prime \prime }-\sin \left (x \right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \begin{align*}
x y^{\prime \prime }+y \sin \left (x \right )&=x \\
y \left (\pi \right ) &= 1 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*}
Series expansion around \(x=\pi \). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.801 |
|
| \begin{align*}
\ln \left (x \right ) y^{\prime \prime }-y \sin \left (x \right )&=0 \\
y \left ({\mathrm e}\right ) &= {\mathrm e}^{-1} \\
y^{\prime }\left ({\mathrm e}\right ) &= 0 \\
\end{align*}
Series expansion around \(x={\mathrm e}\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.742 |
|
| \begin{align*}
y^{\prime \prime \prime }+\sin \left (y\right ) x&=0 \\
y \left (0\right ) &= \frac {\pi }{2} \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[NONE] |
✗ |
✓ |
✗ |
✗ |
0.057 |
|
| \begin{align*}
y^{\prime }-2 y x&=0 \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }+y&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.643 |
|
| \begin{align*}
y^{\prime \prime }-\left (x^{2}+1\right ) y&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \begin{align*}
y^{\prime \prime }&=x^{2} y-y^{\prime } \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
y^{\prime \prime }-y \,{\mathrm e}^{x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.764 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{y}+y x \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✓ |
0.459 |
|
| \begin{align*}
4 x y^{\prime \prime }+2 y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-n y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Jacobi] |
✓ |
✓ |
✓ |
✓ |
1.539 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.398 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.067 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{9}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.367 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.347 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+4 \left (x^{4}-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.015 |
|
| \begin{align*}
x y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{4}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.174 |
|
| \begin{align*}
y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
1.466 |
|
| \begin{align*}
y^{\prime \prime }+\frac {3 y^{\prime }}{x}+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.416 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\cos \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\pi ^{2}-x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=\cos \left (\pi x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\arcsin \left (\sin \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.611 |
|