| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{3}+2 x y^{2}+y+\left (x^{3} y^{2}-2 x^{2} y+x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✗ |
✓ |
17.974 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (3 y-2 x \right ) y^{\prime }-6 y&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
56.033 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y^{2}}{2 y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.223 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y}+x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
✓ |
✓ |
✗ |
133.130 |
|
| \begin{align*}
y^{\prime }&=\sqrt {\frac {5 x -6 y}{5 x +6 y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
101.184 |
|
| \begin{align*}
y^{\prime }+y x&=x^{2}+1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.901 |
|
| \begin{align*}
x^{2} y+2 y^{4}+\left (x^{3}+3 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
27.095 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.496 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.440 |
|
| \begin{align*}
y^{\prime }&=x y^{2}-2 y+4-4 x \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
9.914 |
|
| \begin{align*}
y^{\prime }+y^{2}&=x^{2}+1 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
7.707 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x -1}-\frac {x y}{x -1}+1 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.026 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| \begin{align*}
3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+y&=\sin \left (x \right )+{\mathrm e}^{-x} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.714 |
|
| \begin{align*}
s^{\prime \prime }+b s^{\prime }+\omega ^{2} s&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.643 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }-y&=1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✓ |
4.137 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=\sin \left (2 x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.227 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.012 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=x^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.884 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+y x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
2.353 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=3 \,{\mathrm e}^{x}-2 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.755 |
|
| \begin{align*}
y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y x&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.924 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.458 |
|
| \begin{align*}
4 y^{\prime \prime }-25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
9.612 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.311 |
|
| \begin{align*}
2 y^{\prime \prime \prime }-5 y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.135 |
|
| \begin{align*}
i^{\prime \prime }-4 i^{\prime }+2 i&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.133 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.796 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
y^{\prime \prime \prime }-16 y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \begin{align*}
y^{\prime \prime \prime }+5 y^{\prime \prime }+2 y^{\prime }-12 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.140 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✓ |
✗ |
3.070 |
|
| \begin{align*}
y^{\prime \prime }-\left (m_{1} +m_{2} \right ) y^{\prime }+m_{1} m_{2} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.515 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-20 y^{\prime \prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }-16 y^{\prime \prime }+12 y^{\prime }+12 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.187 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| \begin{align*}
16 y^{\prime \prime }-8 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| \begin{align*}
4 i^{\prime \prime }-12 i^{\prime }+9 i&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \begin{align*}
y^{\left (6\right )}-4 y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.169 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| \begin{align*}
4 y^{\prime \prime \prime \prime }-20 y^{\prime \prime }+25 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.169 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.164 |
|
| \begin{align*}
s^{\prime \prime }+16 s^{\prime }+64 s&=0 \\
s \left (0\right ) &= 0 \\
s^{\prime }\left (0\right ) &= -4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.852 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✓ |
✗ |
0.310 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.300 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=x \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
4.182 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.997 |
|
| \begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
4 y^{\prime \prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.308 |
|
| \begin{align*}
4 y^{\prime \prime }-8 y^{\prime }+7 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+16 y^{\prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.141 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-2 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.076 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.624 |
|
| \begin{align*}
u^{\prime \prime }+16 u&=0 \\
u \left (0\right ) &= 0 \\
u^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.274 |
|
| \begin{align*}
i^{\prime \prime }+2 i^{\prime }+5 i&=0 \\
i \left (0\right ) &= 2 \\
i^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.762 |
|
| \begin{align*}
y^{\left (6\right )}-64 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.132 |
|
| \begin{align*}
y a^{2} b^{2}+\left (a^{2}+b^{2}\right ) y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.223 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.160 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.089 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+25 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.153 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.075 |
|
| \begin{align*}
y^{\left (6\right )}-4 y^{\prime \prime }+4 y^{\prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.119 |
|
| \begin{align*}
s^{\prime \prime \prime \prime }+2 s^{\prime \prime }-8 s&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.149 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.078 |
|
| \begin{align*}
y^{\left (5\right )}-y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.123 |
|
| \begin{align*}
y^{\prime \prime \prime }-4 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.085 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.124 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.142 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y&=0 \\
\end{align*} |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
3.022 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
2.386 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.277 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=4 \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=8 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x}+15 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| \begin{align*}
4 i^{\prime \prime }+i&=t^{2}+2 \cos \left (4 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{x}+\sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.645 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=5 \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.115 |
|
| \begin{align*}
s^{\prime \prime }-3 s^{\prime }+2 s&=8 t^{2}+12 \,{\mathrm e}^{-t} \\
s \left (0\right ) &= 0 \\
s^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.984 |
|
| \begin{align*}
y^{\prime \prime }+y&=6 \cos \left (x \right )^{2} \\
y \left (0\right ) &= 0 \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.303 |
|
| \begin{align*}
L q^{\prime \prime }+R q^{\prime }+\frac {q}{c}&=E_{0} \sin \left (\omega t \right ) \\
q \left (0\right ) &= 0 \\
q^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
9.811 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=4 \sin \left (3 x \right )^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.404 |
|
| \begin{align*}
y^{\prime \prime }+y&=\left \{\begin {array}{cc} x & 0\le x \le \pi \\ 0 & \pi <x \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
8.834 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.803 |
|
| \begin{align*}
y^{\prime \prime }+y&=x^{2}+\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.614 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x^{2}+3 x +{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.832 |
|