| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x -{\mathrm e}^{3 x} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.112 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }-2 y&=\cosh \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.486 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=x^{n} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
28.137 |
|
| \begin{align*}
y^{\prime \prime }-y&=4 \,{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.297 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.234 |
|
| \begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.349 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.292 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }&=f \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.188 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.163 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.160 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.175 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.175 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{3 x} \sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=2 x \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.110 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.104 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x} \ln \left (x \right )}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.306 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{x} \sin \left (x \right ) x \\
\end{align*} | [[_3rd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.172 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 k y^{\prime \prime }+3 k^{2} y^{\prime }+k^{3} y&={\mathrm e}^{-k x} f^{\prime \prime \prime }\left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \sec \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.392 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime }-2 y&=2+x +x \,{\mathrm e}^{-x}+x^{2} {\mathrm e}^{2 x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.399 |
|
| \begin{align*}
-4 y^{\prime }+y^{\prime \prime \prime }&=x^{2}-x \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.095 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }&={\mathrm e}^{-4 x} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.098 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\sin \left (x \right ) \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.353 |
|
| \begin{align*}
y^{\left (6\right )}+y^{\prime \prime \prime \prime }-y&=4 x^{5}-6 x^{2}+2 \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.224 |
|
| \begin{align*}
y^{\left (8\right )}+y&=x^{15} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
5.972 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-2 y&=x^{2}+4 x +3 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.341 |
|
| \begin{align*}
y^{\prime \prime }+3 y&=-x^{6}+x^{4} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.495 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.284 |
|
| \begin{align*}
y^{\left (8\right )}+8 y^{\left (7\right )}+28 y^{\left (6\right )}+56 y^{\left (5\right )}+70 y^{\prime \prime \prime \prime }+56 y^{\prime \prime \prime }+28 y^{\prime \prime }+8 y^{\prime }&={\mathrm e}^{-x} x^{9} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
3.993 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{x} x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| \begin{align*}
y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&={\mathrm e}^{2 x} \cos \left (3 x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.160 |
|
| \begin{align*}
6 x^{2} y^{\prime \prime }-5 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.092 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} | [[_2nd_order, _exact, _linear, _homogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.088 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.103 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.393 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.505 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +\left (3 x -9\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.114 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=6 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.692 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x^{2} y^{\prime }-y x&=2 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.568 |
|
| \begin{align*}
y^{\prime \prime }+p \left (x \right ) y^{\prime }+q \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.529 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime \prime }+\left (-x^{2}+2 x +1\right ) y^{\prime }-\left (x +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.337 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{x} \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.120 |
|
| \begin{align*}
y^{\prime \prime }+y&=x \sin \left (x \right ) \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
y^{\prime \prime \prime }+y&={\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.259 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+16 y&=x^{2}-4 \cos \left (3 x \right ) \\
\end{align*} Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=16 \,{\mathrm e}^{2 x} \\
\end{align*} Using Laplace transform method. |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+54 y^{\prime \prime }-108 y^{\prime }+81 y&=x^{2} {\mathrm e}^{3 x} \\
\end{align*} Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-y^{\prime }+2 y&=-2 x^{4}+x^{2} \\
\end{align*} Using Laplace transform method. |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=\cosh \left (2 x \right ) \\
\end{align*} Using Laplace transform method. |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.186 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=4 x^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✓ | 0.144 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=3 x -6 \\
y \left (0\right ) &= {\frac {1}{3}} \\
y^{\prime }\left (0\right ) &= {\frac {4}{3}} \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.153 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=2 x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.101 |
|
| \begin{align*}
y^{\left (5\right )}&=120 \\
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 ) &= 6 \\
y^{\prime \prime \prime \prime }\left (0\right ) &= 24 \\
\end{align*} Using Laplace transform method. |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \begin{align*}
2 y^{\prime }+y&={\mathrm e}^{x} \\
y \left (2\right ) &= \frac {4 \,{\mathrm e}^{2}}{3} \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.149 |
|
| \begin{align*}
y^{\prime \prime }+y&=x^{2} \\
y \left (\frac {\pi }{2}\right ) &= \frac {\pi ^{2}}{4} \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 2 \pi \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.165 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime }&=x^{3}+{\mathrm e}^{-2 x} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.559 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x +{\mathrm e}^{-x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.928 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=1+\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.272 |
|
| \begin{align*}
y^{\left (10\right )}+y&=x^{10} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
68.570 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{x}+{\mathrm e}^{2 x}+{\mathrm e}^{3 x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.169 |
|
| \begin{align*}
x^{\prime }-x-y^{\prime }&=0 \\
y^{\prime }+3 x-2 y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.535 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&=12 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.452 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+y&=x^{5}+2 x^{2} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.116 |
|
| \begin{align*}
y^{\prime \prime }+i y&=\cosh \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.702 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=x -4 \\
y \left (0\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.489 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }-5 y&=x^{2} {\mathrm e}^{-x} \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.329 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-y&=\sinh \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.647 |
|
| \begin{align*}
y^{\left (6\right )}+y&=x^{7}+2 x^{3} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.383 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.401 |
|
| \begin{align*}
x-y+z^{\prime }&=0 \\
x^{\prime }-y&=1 \\
y^{\prime }-y+z&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.891 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+a x y^{\prime }+b y&=f \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
5.029 |
|
| \begin{align*}
4 y^{\prime \prime }+x^{2} y^{\prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.262 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.255 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+3 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.226 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +20 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +56 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
4 \left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| \begin{align*}
y^{\prime \prime }+3 x^{3} y^{\prime }+x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.264 |
|
| \begin{align*}
\left (x^{3}+8\right ) y^{\prime \prime }+3 x^{2} y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| \begin{align*}
\left (x^{3}-8\right ) y^{\prime \prime }-4 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.286 |
|
| \begin{align*}
y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.021 |
|
| \begin{align*}
\left (-x^{4}+1\right ) y^{\prime \prime \prime }-24 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✗ |
✓ |
✓ |
✗ |
0.021 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }-x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). | [[_Emden, _Fowler]] | ✓ | ✓ | ✓ | ✓ | 0.353 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime }-y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.021 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime }+\frac {x^{2} y^{\prime \prime }}{x +1}-\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.025 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime }-\frac {x^{2} y^{\prime }}{x +1}+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.024 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.488 |
|
| \begin{align*}
x^{2} y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✗ |
✗ |
✓ |
✗ |
0.040 |
|
| \begin{align*}
y^{\prime } x +\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✗ |
0.194 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x -5 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.337 |
|
| \begin{align*}
2 y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.461 |
|
| \begin{align*}
25 x^{2} y^{\prime \prime }+\left (4+2 x \right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.442 |
|