| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.685 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.582 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.405 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=4 x^{2}+2 x +3 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.714 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=52 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }-5 y&=30 \,{\mathrm e}^{-4 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{\frac {x}{2}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.084 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=-5 \,{\mathrm e}^{3 x} \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=10 \cos \left (2 x \right )+15 \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=25 \sin \left (6 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=26 \cos \left (\frac {x}{3}\right )-12 \sin \left (\frac {x}{3}\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.210 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }-5 y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=-4 \cos \left (x \right )+7 \sin \left (x \right ) \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.651 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=-200 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }-5 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=18 x^{2}+3 x +4 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=9 x^{4}-9 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=x^{3} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=25 x \cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=54 x^{2} {\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \begin{align*}
y^{\prime \prime }&=6 \,{\mathrm e}^{x} \sin \left (x \right ) x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.201 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\left (-6 x -8\right ) \cos \left (2 x \right )+\left (8 x -11\right ) \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.020 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\left (12 x -4\right ) {\mathrm e}^{-5 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=39 x \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=-3 \,{\mathrm e}^{-2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.474 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=20 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.108 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=3 \sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.534 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=10 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.565 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=\left (72 x^{2}-1\right ) {\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.508 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=4 x \,{\mathrm e}^{6 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| \begin{align*}
y^{\prime \prime }-10 y^{\prime }+25 y&=6 \,{\mathrm e}^{5 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.567 |
|
| \begin{align*}
y^{\prime \prime }-10 y^{\prime }+25 y&=6 \,{\mathrm e}^{-5 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=24 \sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=8 \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{-x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=100 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&={\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=10 x^{2}+4 x +8 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
y^{\prime \prime }+9 y&={\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| \begin{align*}
y^{\prime \prime }+y&=6 \cos \left (x \right )-3 \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \begin{align*}
y^{\prime \prime }+y&=6 \cos \left (2 x \right )-3 \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.597 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=x^{3} {\mathrm e}^{-x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=x^{3} {\mathrm e}^{2 x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{-7 x}+2 \,{\mathrm e}^{-7 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-8 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.463 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} \cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.007 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+20 y&={\mathrm e}^{4 x} \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+20 y&={\mathrm e}^{2 x} \sin \left (4 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+20 y&=x^{3} \sin \left (4 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.918 |
|
| \begin{align*}
y^{\prime \prime }-10 y^{\prime }+25 y&=3 x^{2} {\mathrm e}^{5 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| \begin{align*}
y^{\prime \prime }-10 y^{\prime }+25 y&=3 x^{4} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=12 \,{\mathrm e}^{-2 x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=10 \sin \left (2 x \right ) \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.168 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=32 \,{\mathrm e}^{4 x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.153 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=32 x \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=x^{2} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=30 \cos \left (2 x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.170 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=6 \,{\mathrm e}^{x} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.158 |
|
| \begin{align*}
y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} {\mathrm e}^{3 x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| \begin{align*}
y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} \sin \left (3 x \right ) \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right ) \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=30 x \cos \left (2 x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.281 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=3 x \cos \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.635 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=3 x \,{\mathrm e}^{x} \cos \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.246 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=5 x^{5} {\mathrm e}^{2 x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.200 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=27 \,{\mathrm e}^{6 x}+25 \sin \left (6 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=25 x \cos \left (2 x \right )+3 \sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.240 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=5 \sin \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+5 y&=20 \sinh \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y&=\frac {5}{x^{3}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.921 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=\frac {50}{x^{3}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.088 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=85 \cos \left (2 \ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
17.519 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y&=15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.636 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y&=4 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
12.109 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=\frac {10}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
11.454 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=6 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
7.224 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=64 x^{2} \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
6.303 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=3 \sqrt {x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.391 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cot \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\csc \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }+10 y&=6 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\left (24 x^{2}+2\right ) {\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.613 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{-2 x}}{x^{2}+1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.689 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=\sqrt {x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.263 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=12 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.391 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.333 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y&=\frac {1}{x -2} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| \begin{align*}
x y^{\prime \prime }-y^{\prime }-4 x^{3} y&=x^{3} {\mathrm e}^{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.579 |
|
| \begin{align*}
x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y&=8 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.895 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }+x y^{\prime }-y&=\left (x +1\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.470 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y&=\frac {10}{x} \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= -15 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.180 |
|