| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y+\sqrt {y x}-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.445 |
|
| \begin{align*}
y^{\prime } x -\sqrt {x^{2}-y^{2}}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.450 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.557 |
|
| \begin{align*}
x^{2}+2 y x -y^{2}+\left (y^{2}+2 y x -x^{2}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✗ |
11.288 |
|
| \begin{align*}
-y+y^{\prime } x&=y^{\prime } y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.164 |
|
| \begin{align*}
y^{2}+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
11.697 |
|
| \begin{align*}
x^{2}+y x +y^{2}&=x^{2} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.427 |
|
| \begin{align*}
\frac {1}{x^{2}-y x +y^{2}}&=\frac {y^{\prime }}{2 y^{2}-y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
38.271 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y}{3 x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.325 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.289 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.720 |
|
| \begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.145 |
|
| \begin{align*}
y^{\prime } x&=y \ln \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.070 |
|
| \begin{align*}
y^{\prime } \left (y^{\prime }+y\right )&=x \left (x +y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.276 |
|
| \begin{align*}
\left (y^{\prime } x +y\right )^{2}&=y^{2} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
54.496 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-3 x y^{\prime } y+2 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {y^{2}+x^{2}} \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, _dAlembert] | ✓ | ✓ | ✓ | ✓ | 10.908 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.495 |
|
| \begin{align*}
y^{\prime }+\frac {x +2 y}{x}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.796 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.290 |
|
| \begin{align*}
y^{\prime } x&=x +\frac {y}{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
11.578 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-2}{y-x -4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.463 |
|
| \begin{align*}
2 x -4 y+6+\left (x +y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
21.205 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y-x +5}{2 x -y-4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 x +3 y+15}{2 x +y+7} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
37.950 |
|
| \begin{align*}
y^{\prime }&=\frac {x +3 y-5}{x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.402 |
|
| \begin{align*}
y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y+1\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
2.768 |
|
| \begin{align*}
2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.958 |
|
| \begin{align*}
x -y-1+\left (y-x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \begin{align*}
\left (x +4 y\right ) y^{\prime }&=2 x +3 y-5 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.180 |
|
| \begin{align*}
y+2&=\left (2 x +y-4\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.169 |
|
| \begin{align*}
\left (1+y^{\prime }\right ) \ln \left (\frac {x +y}{x +3}\right )&=\frac {x +y}{x +3} \\
\end{align*} | [[_homogeneous, ‘class C‘], _exact, _dAlembert] | ✓ | ✓ | ✓ | ✓ | 7.491 |
|
| \begin{align*}
y^{\prime }&=\frac {x -2 y+5}{-4-2 x +y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -y+1}{2 x +y+4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
43.230 |
|
| \begin{align*}
2 y^{\prime } x +\left (1+x^{2} y^{4}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.920 |
|
| \begin{align*}
2 x \left (x -y^{2}\right ) y^{\prime }+y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
x^{3} \left (y^{\prime }-x \right )&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
0.230 |
|
| \begin{align*}
2 x^{2} y^{\prime }&=y^{3}+y x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
y+x \left (2 y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| \begin{align*}
2 y^{\prime }+x&=4 \sqrt {y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
✓ |
✓ |
✗ |
0.764 |
|
| \begin{align*}
y^{\prime }&=y^{2}-\frac {2}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
2 y^{\prime } x +y&=y^{2} \sqrt {x -y^{2} x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
1.766 |
|
| \begin{align*}
\frac {2 x y^{\prime } y}{3}&=\sqrt {x^{6}-y^{4}}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
1.455 |
|
| \begin{align*}
2 y+\left (x^{2} y+1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
0.286 |
|
| \begin{align*}
x \left (-y x +1\right ) y^{\prime }+\left (y x +1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| \begin{align*}
\left (y^{2} x^{2}+1\right ) y+\left (y^{2} x^{2}-1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
\left (x^{2}-y^{4}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
y \left (1+\sqrt {x^{2} y^{4}-1}\right )+2 y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
x \left (2-9 x y^{2}\right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} | [_exact, _rational] | ✓ | ✓ | ✓ | ✗ | 2.073 |
|
| \begin{align*}
\frac {y}{x}+\left (y^{3}+\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.938 |
|
| \begin{align*}
3+2 x +\left (-2+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.108 |
|
| \begin{align*}
2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
7.122 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.238 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.471 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.822 |
|
| \begin{align*}
y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+y \cos \left (x \right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
1.941 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+x^{2} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.295 |
|
| \begin{align*}
y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.632 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime } x +4 x^{2} y^{\prime }+8 x^{3} y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.037 |
|
| \begin{align*}
y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+{\mathrm e}^{x} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.443 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.137 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }-x^{2} y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.713 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=2 x \,{\mathrm e}^{x}-1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.164 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime } x -y&=x^{2}+2 x \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 1.213 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2}+2 x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.007 |
|
| \begin{align*}
-y+y^{\prime } x +x^{3} y^{\prime \prime }&=\cos \left (\frac {1}{x}\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.096 |
|
| \begin{align*}
x \left (x +1\right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }-y&=x +\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.624 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (x -2\right ) y^{\prime }-y&=x^{2}-1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.855 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (4 x +3\right ) y^{\prime }-y&=x +\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
88.898 |
|
| \begin{align*}
x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-y^{\prime } x +y&=x \left (1-\ln \left (x \right )\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.852 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=\sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.877 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\frac {y}{4}&=-\frac {x^{2}}{2}+\frac {1}{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.339 |
|
| \begin{align*}
\left (\cos \left (x \right )+\sin \left (x \right )\right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }+\left (-\sin \left (x \right )+\cos \left (x \right )\right ) y&=\left (\cos \left (x \right )+\sin \left (x \right )\right )^{2} {\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.147 |
|
| \begin{align*}
\left (-\sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-2 \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) y&=\left (-\sin \left (x \right )+\cos \left (x \right )\right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
7.480 |
|
| \begin{align*}
y^{\prime }&=x^{2} \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.790 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{1-y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.460 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{2}+4 x +2}{-2+2 y} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.691 |
|
| \begin{align*}
y^{\prime } x -2 \sqrt {y x}&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.144 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y-1}{x -y+3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.757 |
|
| \begin{align*}
{\mathrm e}^{x}+y+\left (x -2 \sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
2.841 |
|
| \begin{align*}
3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.131 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, _Bernoulli] | ✓ | ✓ | ✓ | ✓ | 3.483 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.658 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{2 x}+\frac {x^{2}}{2 y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.265 |
|
| \begin{align*}
y^{\prime }&=-\frac {2}{t}+\frac {y}{t}+\frac {y^{2}}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.972 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{t}-1-y^{2} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
2.985 |
|
| \begin{align*}
y^{\prime } y+x&=a {y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.211 |
|
| \begin{align*}
{y^{\prime }}^{2}-a^{2} y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.260 |
|
| \begin{align*}
{y^{\prime }}^{2}&=4 x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \begin{align*}
s^{\prime \prime }+2 s^{\prime }+s&=0 \\
s \left (0\right ) &= 4 \\
s^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.239 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=1+3 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.289 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
y^{\prime \prime }+y&=4 \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.384 |
|
| \begin{align*}
p \,x^{2} u^{\prime \prime }+q x u^{\prime }+r u&=f \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.026 |
|
| \begin{align*}
\sin \left (x \right ) u^{\prime \prime }+2 \cos \left (x \right ) u^{\prime }+\sin \left (x \right ) u&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✗ |
0.512 |
|