| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
2 x^{2}+2 y^{2}+x +\left (y+x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.308 |
|
| \begin{align*}
5 x -y+3 x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.467 |
|
| \begin{align*}
x y^{\prime }+y&=3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.602 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.560 |
|
| \begin{align*}
x^{2}+y^{2}+1-2 x y y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.425 |
|
| \begin{align*}
-x^{2} y+\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.591 |
|
| \begin{align*}
2 x -3 y+\left (7 y^{2}+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
55.146 |
|
| \begin{align*}
3 y+\left (7 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.363 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}}-\frac {y}{x}+y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.624 |
|
| \begin{align*}
y x -\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.997 |
|
| \begin{align*}
y x +1+y^{2} y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
111.970 |
|
| \begin{align*}
x -y+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.425 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.709 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y+2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.595 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y-4}{x -y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.463 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x -2 y+7}{2 x +3 y+9} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.398 |
|
| \begin{align*}
y^{\prime }&=\frac {5 x -y-2}{x +y+4} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.174 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+5}{2 x -y-3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
32.261 |
|
| \begin{align*}
y^{\prime }&=\frac {y-x +1}{3 x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.095 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x -y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.653 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{x -y+1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.766 |
|
| \begin{align*}
y^{\prime }&=-\frac {x +2 y}{y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
6.926 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.413 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {2}\, \sqrt {\frac {x +y}{x}}}{2} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
61.371 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y-4}{x -y+1} \\
y \left (2\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.941 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.979 |
|
| \begin{align*}
y^{\left (5\right )}-y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {1+{y^{\prime }}^{2}}{2 y} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
0.708 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.183 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }&=3 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \begin{align*}
y^{\left (5\right )}-\frac {y^{\prime \prime \prime \prime }}{x}&=0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }&=1 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.095 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.338 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-2 y y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.256 |
|
| \begin{align*}
y^{\prime \prime }-\frac {2 y^{\prime }}{y^{3}}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.092 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {1+{y^{\prime }}^{2}}{y} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
3.909 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.500 |
|
| \begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
3.040 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.245 |
|
| \begin{align*}
y^{\prime \prime \prime }+x^{2} y&={\mathrm e}^{x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
0.053 |
|
| \begin{align*}
y^{\prime \prime }+y y^{\prime \prime \prime \prime }&=5 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.043 |
|
| \begin{align*}
y^{\prime \prime }+\cos \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
32.626 |
|
| \begin{align*}
y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y&=2 x^{2}+3 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.164 |
|
| \begin{align*}
y-x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.915 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x^{2}}&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
6.052 |
|
| \begin{align*}
2 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }+y x&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.051 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }-2&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
y^{\prime }+\sqrt {y}&=3 x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
✓ |
✗ |
✗ |
10.328 |
|
| \begin{align*}
y^{\prime \prime }+y x&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| \begin{align*}
2 y-3 x y^{\prime \prime }+4 y^{\prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| \begin{align*}
y^{\prime \prime \prime }&=2 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.086 |
|
| \begin{align*}
{\mathrm e}^{x} {y^{\prime }}^{2}+3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.645 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }-6 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.277 |
|
| \begin{align*}
y y^{\prime }&=3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.578 |
|
| \begin{align*}
x y^{\prime \prime \prime }+4 x y^{\prime \prime }-y x&=1 \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
0.051 |
|
| \begin{align*}
7 y^{\prime }-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.558 |
|
| \begin{align*}
\left (1+a \cos \left (2 x \right )\right ) y^{\prime \prime }+\lambda y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
52.802 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.036 |
|
| \begin{align*}
y^{\prime \prime \prime }&=x^{3} \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.127 |
|
| \begin{align*}
y^{\prime \prime }&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \begin{align*}
y^{\prime \prime }&=3 x \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.041 |
|
| \begin{align*}
y^{\prime \prime \prime }&=x^{2} \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.110 |
|
| \begin{align*}
y^{\left (5\right )}&=0 \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.042 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.327 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.336 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.771 |
|
| \begin{align*}
x y^{\prime }+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.894 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.277 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.372 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.619 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| \begin{align*}
2 y^{\prime \prime }-3 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.277 |
|
| \begin{align*}
x y^{\prime \prime }-3 y^{\prime }-5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| \begin{align*}
y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
48.357 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime \prime }+2 \left (2 x -a -b \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.813 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.700 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.286 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.872 |
|
| \begin{align*}
3 y^{\prime \prime }+48 y^{\prime }+192 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \begin{align*}
x y^{\prime \prime }+4 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.857 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.867 |
|
| \begin{align*}
x y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✗ |
✗ |
✗ |
✗ |
11.137 |
|
| \begin{align*}
x y^{\prime \prime }+y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }-x y^{\prime }+y \,{\mathrm e}^{x}&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
93.184 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+y&=2 \\
y \left (\frac {3 \pi }{4}\right ) &= 1 \\
y^{\prime }\left (\frac {3 \pi }{4}\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
69.351 |
|
| \begin{align*}
\left (x^{3}-1\right ) y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y x&=0 \\
y \left (-1\right ) &= 0 \\
y^{\prime }\left (-1\right ) &= 2 \\
y^{\prime \prime }\left (-1\right ) &= 2 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.653 |
|
| \begin{align*}
y y^{\prime }+y^{\prime \prime }&=2 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
25.283 |
|
| \begin{align*}
3 y^{\prime \prime }+y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime \prime }+3 y&=1 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
29.102 |
|
| \begin{align*}
y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x}&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
41.158 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.911 |
|
| \begin{align*}
2 x y^{\prime \prime }-7 \cos \left (x \right ) y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
73.355 |
|
| \begin{align*}
y^{\prime \prime }+4 \tan \left (x \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
30.803 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime \prime }+y&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
✗ |
31.252 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+3 x^{3} y^{\prime }+\frac {4 y}{x -1}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
260.213 |
|