| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=8 \cos \left (2 x \right )-4 x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=x +\sin \left (x \right )+\cos \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.696 |
|
| \begin{align*}
i^{\prime \prime }+9 i&=12 \cos \left (3 t \right ) \\
i \left (0\right ) &= 4 \\
i^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.892 |
|
| \begin{align*}
s^{\prime \prime }+s^{\prime }&=t +{\mathrm e}^{-t} \\
s \left (0\right ) &= 0 \\
s^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.648 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=\cosh \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| \begin{align*}
y^{\prime \prime }+y&=x \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.969 |
|
| \begin{align*}
y^{\prime \prime }+\omega ^{2} y&=A \cos \left (\lambda x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.060 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\sin \left (x \right )^{4} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.431 |
|
| \begin{align*}
y^{\prime \prime }+y&=x \,{\mathrm e}^{-x}+3 \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.876 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=\sin \left (2 x \right ) x +x^{3} {\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.879 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=3 x^{2}-4 \,{\mathrm e}^{x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-y&={\mathrm e}^{x} x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.495 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) {\mathrm e}^{-x}+2 x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.849 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=3 \,{\mathrm e}^{x}+2 \,{\mathrm e}^{-x}+x^{3} {\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.429 |
|
| \begin{align*}
y^{\prime \prime }-y&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=x^{2}+3 x \cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=\sin \left (3 x \right )+x \,{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.046 |
|
| \begin{align*}
q^{\prime \prime }+q&=t \sin \left (t \right )+\cos \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.189 |
|
| \begin{align*}
y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+24 y&=x^{2} {\mathrm e}^{3 x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.271 |
|
| \begin{align*}
y^{\prime \prime }+\omega ^{2} y&=t \left (\sin \left (\omega t \right )+\cos \left (\omega t \right )\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.974 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \left (1+\cos \left (2 x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\cos \left (x \right ) \cos \left (2 x \right ) \cos \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.602 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }-6 y^{\prime }-12 y&=\sinh \left (x \right )^{4} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.238 |
|
| \begin{align*}
y^{\prime \prime }+y&=x^{2} \cos \left (5 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.620 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\csc \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=3 \,{\mathrm e}^{-2 x}+x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.503 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.974 |
|
| \begin{align*}
2 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.459 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x} x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{-x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\sqrt {x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.224 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{x}+{\mathrm e}^{-x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.430 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \,{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
30.336 |
|
| \begin{align*}
y^{\prime \prime }-y&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
6.401 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.573 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x}-{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| \begin{align*}
y^{\prime \prime }-y&=2 x^{4}-3 x +1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=4 x^{3}-2 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.330 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-x}+1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x} \sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime }&=x^{5}+1 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&={\mathrm e}^{4 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y&=2 \,{\mathrm e}^{3 x}-4 \,{\mathrm e}^{-5 x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=x^{3} {\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=2 x^{2} {\mathrm e}^{-2 x}+3 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.552 |
|
| \begin{align*}
y^{\prime \prime }+y&=x^{2} \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.352 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.644 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y&=x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
49.295 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=x^{2}+16 \ln \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
22.251 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y&=16 \sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.418 |
|
| \begin{align*}
t^{2} i^{\prime \prime }+2 i^{\prime } t +i&=t \ln \left (t \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
31.173 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {\frac {4 x}{25}-\frac {4 y}{25}}{x^{2}} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.739 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=\sqrt {x}+\frac {1}{\sqrt {x}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.654 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x&=5 \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.303 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x +1 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
-y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=x \ln \left (x \right ) \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+y^{\prime } x -y&=1 \\
\end{align*} |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=x^{2}-4 x +2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.328 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.120 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.679 |
|
| \begin{align*}
\left (3+2 x \right )^{2} y^{\prime \prime }+\left (3+2 x \right ) y^{\prime }-2 y&=24 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.301 |
|
| \begin{align*}
\left (2+x \right )^{2} y^{\prime \prime }-y&=4 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.549 |
|
| \begin{align*}
\left (r^{2}+r \right ) R^{\prime \prime }+r R^{\prime }-n \left (n +1\right ) R&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
132.403 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
5.217 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.124 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 x -2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
60.492 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime \prime }+\left (3 \sin \left (x \right )^{2}-\cos \left (x \right )\right ) y^{\prime }+2 \sin \left (x \right )^{3} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
8.671 |
|
| \begin{align*}
x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y&=\frac {1}{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.826 |
|
| \begin{align*}
y^{\prime \prime }+3 y&=x^{2}+1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.713 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x}+{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| \begin{align*}
y^{\prime \prime \prime }-4 y&=4 x +2+3 \,{\mathrm e}^{-2 x} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.210 |
|
| \begin{align*}
i^{\prime \prime }+2 i^{\prime }+5 i&=34 \cos \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }-x&=8 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.192 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-6 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.457 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }&=1 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.213 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+16 y^{\prime \prime }&=64 \cos \left (4 x \right ) \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=x \left (\cos \left (x \right )+1\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.348 |
|
| \begin{align*}
r^{\prime \prime }-2 r&=-{\mathrm e}^{-2 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.503 |
|
| \begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime }&=12 \,{\mathrm e}^{2 x}+24 x^{2} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.269 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.361 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=24 x +24 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
55.168 |
|
| \begin{align*}
s^{\prime \prime \prime \prime }-2 s^{\prime \prime }+s&=100 \cos \left (3 t \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.251 |
|
| \begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.965 |
|
| \begin{align*}
y^{\left (5\right )}-5 y^{\prime \prime }+4 y^{\prime }&=x^{2}-x +{\mathrm e}^{x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
i^{\prime \prime \prime \prime }+9 i^{\prime \prime }&=20 \,{\mathrm e}^{-t} \\
i \left (0\right ) &= 0 \\
i^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.274 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime }-y^{\prime \prime } x +y^{\prime }&=\frac {\ln \left (x \right )}{x} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.341 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y&=64 \sin \left (2 x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.651 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\
y \left (\frac {1}{2}\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.548 |
|
| \begin{align*}
y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\left (1+\sin \left (x \right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.619 |
|
| \begin{align*}
y^{\prime \prime \prime }&=\frac {24 x +24 y}{x^{3}} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✓ |
0.054 |
|
| \begin{align*}
x y^{\prime \prime \prime }+2 y^{\prime \prime } x -y^{\prime } x -2 y x&=1 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✓ |
0.056 |
|