| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
3 y^{\prime \prime }+4 y^{\prime }-4 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \begin{align*}
4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 9 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 7 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \begin{align*}
9 y^{\prime \prime }-6 y^{\prime }+y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+29 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+58 y&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \begin{align*}
9 y^{\prime \prime }+6 y^{\prime }+5 y&=0 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+37 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.145 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -8 \\
y^{\prime \prime }\left (0\right ) &= -4 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.131 |
|
| \begin{align*}
y^{\prime \prime \prime }-5 y^{\prime \prime }+9 y^{\prime }-5 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 6 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.122 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+6 y^{\prime \prime }+2 y^{\prime }+5 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.091 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }+13 y^{\prime }+30 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.086 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+8 y&=4 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.624 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-8 y&=4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=6 \sin \left (2 x \right )+7 \cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.573 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=10 \sin \left (4 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.713 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+4 y&=\cos \left (4 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \begin{align*}
-4 y-3 y^{\prime }+y^{\prime \prime }&=16 x -12 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+5 y&=2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=5 \,{\mathrm e}^{-2 x} x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }+y^{\prime }-6 y&=-18 x^{2}+1 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y&=8 \,{\mathrm e}^{-2 x} x \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.175 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }-5 y&=5 \sin \left (2 x \right )+10 x^{2}+3 x +7 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \begin{align*}
4 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+3 y&=3 x^{3}-8 x \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.175 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.875 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x}-4 x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=4 \,{\mathrm e}^{x}-18 \,{\mathrm e}^{-x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.242 |
|
| \begin{align*}
2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=9 \,{\mathrm e}^{2 x}-8 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=2 x^{2}+4 \sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime }&=3 \,{\mathrm e}^{-x}+6 \,{\mathrm e}^{2 x}-6 x \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.280 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{4 x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.294 |
|
| \begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=3 \,{\mathrm e}^{x} x^{2}-7 \,{\mathrm e}^{x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.208 |
|
| \begin{align*}
y^{\prime \prime }+y&=x \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=12 x^{2}-16 x \cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }&=18 x^{2}+16 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x}-9 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+7 y^{\prime \prime }-5 y^{\prime }+6 y&=5 \sin \left (x \right )-12 \sin \left (2 x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.059 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=9 x^{2}+4 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.674 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+4 y&=16 x +20 \,{\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+15 y&=9 x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 10 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.715 |
|
| \begin{align*}
y^{\prime \prime }+7 y^{\prime }+10 y&=4 x \,{\mathrm e}^{-3 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \begin{align*}
16 y+8 y^{\prime }+y^{\prime \prime }&=8 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=27 \,{\mathrm e}^{-6 x} \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=18 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| \begin{align*}
y^{\prime \prime }-10 y^{\prime }+29 y&=8 \,{\mathrm e}^{5 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=8 \sin \left (3 x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.831 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 x \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.040 |
|
| \begin{align*}
y^{\prime \prime }-y&=3 \,{\mathrm e}^{x} x^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.822 |
|
| \begin{align*}
y^{\prime \prime }+y&=3 x^{2}-4 \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=8 \sin \left (2 x \right ) \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=3 x \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}-\sin \left (x \right ) \\
y \left (0\right ) &= {\frac {33}{40}} \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }-4 y&=8 x^{2}+3-6 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 7 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.260 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&=x^{3}+x +{\mathrm e}^{-2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| \begin{align*}
y^{\prime \prime }+9 y&={\mathrm e}^{3 x}+{\mathrm e}^{-3 x}+{\mathrm e}^{3 x} \sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.533 |
|
| \begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \left (\cos \left (x \right )+1\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} x^{4}+x^{3} {\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.214 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&=x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.707 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&={\mathrm e}^{x} x^{2}+3 x \,{\mathrm e}^{2 x}+5 x^{2} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=x \,{\mathrm e}^{2 x}+x^{2} {\mathrm e}^{3 x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+4 y^{\prime \prime }+3 y^{\prime }+y&=x^{2} {\mathrm e}^{-x}+3 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.306 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-16 y&=x^{2} \sin \left (2 x \right )+x^{4} {\mathrm e}^{2 x} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| \begin{align*}
y^{\left (6\right )}+2 y^{\left (5\right )}+5 y^{\prime \prime \prime \prime }&=x^{3}+x^{2} {\mathrm e}^{-x}+\sin \left (2 x \right ) {\mathrm e}^{-x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.470 |
|
| \begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=x^{2} \cos \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.971 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+16 y&=x \,{\mathrm e}^{\sqrt {2}\, x} \sin \left (\sqrt {2}\, x \right )+{\mathrm e}^{-\sqrt {2}\, x} \cos \left (\sqrt {2}\, x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.461 |
|
| \begin{align*}
-4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=\cos \left (x \right )^{2}-\cosh \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y&=\sin \left (2 x \right ) \sin \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.828 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\sec \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \tan \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.758 |
|
| \begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.688 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{x} \tan \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.859 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 x}}{x^{3}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right ) \sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.863 |
|
| \begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right )^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.750 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\frac {1}{{\mathrm e}^{x}+1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.623 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\frac {1}{{\mathrm e}^{2 x}+1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.691 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {1}{1+\sin \left (x \right )} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \arcsin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.815 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\frac {{\mathrm e}^{-x}}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-6 y^{\prime } x +10 y&=3 x^{4}+6 x^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.682 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.863 |
|
| \begin{align*}
\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=\left (2+x \right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.650 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.263 |
|
| \begin{align*}
x \left (x -2\right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (x -1\right ) y&=3 x^{2} \left (x -2\right )^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.467 |
|
| \begin{align*}
\left (2 x +1\right ) \left (x +1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=\left (2 x +1\right )^{2} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.979 |
|
| \begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y&=\sin \left (x \right )^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.218 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&={\mathrm e}^{x} x^{2} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.227 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.101 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.474 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.026 |
|