| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=\frac {\sqrt {x +y}+\sqrt {x -y}}{-\sqrt {x -y}+\sqrt {x +y}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
47.717 |
|
| \begin{align*}
y^{\prime }&=\frac {1+\sqrt {x -y}}{1-\sqrt {x -y}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.090 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
29.094 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{5}+3 x^{2} y^{2}}{2 x^{3} y-2 y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
10.822 |
|
| \begin{align*}
2+3 x y^{2}-4 x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.563 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x -3 y-5\right )^{2}}{\left (x +y-1\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
24.027 |
|
| \begin{align*}
\sqrt {x +y+1}\, y^{\prime }&=\sqrt {x +y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
45.534 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y x +1\right )}{x \left (-y x +1\right )} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
107.552 |
|
| \begin{align*}
x y^{\prime }-y&=\arctan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
11.243 |
|
| \begin{align*}
3 x +4 y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.371 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
44.822 |
|
| \begin{align*}
2 x y y^{\prime }&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.336 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{x +y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
47.763 |
|
| \begin{align*}
y^{\prime }&=\frac {x -\cos \left (x \right ) y}{\sin \left (x \right )+y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
12.754 |
|
| \begin{align*}
r^{\prime }&=\frac {r \sin \left (t \right )}{2 r \cos \left (t \right )-1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
31.167 |
|
| \begin{align*}
{\mathrm e}^{-x} y-\sin \left (x \right )-\left ({\mathrm e}^{-x}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
31.992 |
|
| \begin{align*}
x^{2}+\frac {y}{x}+\left (\ln \left (x \right )+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
11.719 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y-{\mathrm e}^{x}\right )}{{\mathrm e}^{x}-2 y x} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
11.807 |
|
| \begin{align*}
\left (x^{2}+x \right ) y^{\prime }+2 x +1+2 \cos \left (x \right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \begin{align*}
y^{\prime }&=\frac {y-2 x}{-x +2 y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
42.015 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=0 \\
y \left (1\right ) &= -3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.926 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x -\sin \left (y\right )}{x \cos \left (y\right )} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
6.437 |
|
| \begin{align*}
y^{\prime }&=\frac {2 \sin \left (2 x \right )-\tan \left (y\right )}{x \sec \left (y\right )^{2}} \\
y \left (\pi \right ) &= \frac {\pi }{4} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
31.608 |
|
| \begin{align*}
\left (x^{2}+2 y \,{\mathrm e}^{2 x}\right ) y^{\prime }+2 y x +2 y^{2} {\mathrm e}^{2 x}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
21.475 |
|
| \begin{align*}
y^{2}+2 x^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.763 |
|
| \begin{align*}
y+\left (4 x -y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
28.680 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }-2 y \sin \left (x \right )+3&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.970 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.158 |
|
| \begin{align*}
\frac {y}{\left (x +y\right )^{2}}-1+\left (1-\frac {x}{\left (x +y\right )^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
15.090 |
|
| \begin{align*}
x y^{2}+2 y+\left (3 x^{2} y-4 x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
222.692 |
|
| \begin{align*}
3 x +2 y^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.781 |
|
| \begin{align*}
2 x^{3}-y+x y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.362 |
|
| \begin{align*}
y^{2} \cos \left (x \right )-y+\left (x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
28.361 |
|
| \begin{align*}
\left (x +x^{3} \sin \left (2 y\right )\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
5.645 |
|
| \begin{align*}
y^{\prime }&=\frac {\sin \left (y\right )}{x \cos \left (y\right )-\sin \left (y\right )^{2}} \\
y \left (0\right ) &= \frac {\pi }{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
27.663 |
|
| \begin{align*}
2 y \sin \left (x \right )-\cos \left (x \right )^{3}+\cos \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.549 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x}&=x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.408 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{y^{3}-3 x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
30.994 |
|
| \begin{align*}
i^{\prime }&=\frac {t -i t}{t^{2}+1} \\
i \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.033 |
|
| \begin{align*}
y^{3}+2 y \,{\mathrm e}^{x}+\left ({\mathrm e}^{x}+3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
7.474 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{x} \\
y \left (3\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.667 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y^{2} \cot \left (x \right )+\sin \left (x \right ) \cos \left (x \right )}{2 y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.474 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{x^{2} y+y^{3}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
6.901 |
|
| \begin{align*}
3 x^{2}+y+3 x^{3} y+x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.723 |
|
| \begin{align*}
2 x +2 x y^{2}+\left (x^{2} y+2 y+3 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
6.842 |
|
| \begin{align*}
y^{2}+y x +1+\left (x^{2}+y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
13.652 |
|
| \begin{align*}
2 y^{2}+4 x^{2} y+\left (4 y x +3 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
183.906 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
14.799 |
|
| \begin{align*}
x y^{\prime }+3 y&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.454 |
|
| \begin{align*}
y^{2}+x y y^{\prime }&=\left (2 y^{2}+1\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
6.748 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=x^{2} \sin \left (3 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.572 |
|
| \begin{align*}
i^{\prime }+3 i&={\mathrm e}^{-2 t} \\
i \left (0\right ) &= 5 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.990 |
|
| \begin{align*}
y^{\prime }+y \cot \left (x \right )&=\cos \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.167 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x -3 y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.938 |
|
| \begin{align*}
r^{\prime }&=t -\frac {r}{3 t} \\
r \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
11.527 |
|
| \begin{align*}
i^{\prime }+2 i&=10 \,{\mathrm e}^{-2 t} \\
i \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.882 |
|
| \begin{align*}
y^{\prime }-y&=x y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.062 |
|
| \begin{align*}
y^{2}+\left (-x^{3}+y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
119.921 |
|
| \begin{align*}
x y^{\prime \prime }-3 y^{\prime }&=4 x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.145 |
|
| \begin{align*}
x y^{\prime }&=2 x^{2} y+\ln \left (y\right ) y \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
12.086 |
|
| \begin{align*}
x y^{\prime }+3&=4 x \,{\mathrm e}^{-y} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
21.836 |
|
| \begin{align*}
y+\left (2 x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
54.575 |
|
| \begin{align*}
y+\left (y^{3}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
19.782 |
|
| \begin{align*}
y+x^{3}+x y^{2}-x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
9.264 |
|
| \begin{align*}
x^{3}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
17.098 |
|
| \begin{align*}
x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
97.595 |
|
| \begin{align*}
x^{2}+y^{2}+y+\left (x^{2}+y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
5.468 |
|
| \begin{align*}
x -x^{2}-y^{2}+\left (y+x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
4.826 |
|
| \begin{align*}
x^{2} y+y^{3}-x +\left (x^{3}-y+x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
6.164 |
|
| \begin{align*}
y-x \sqrt {x^{2}+y^{2}}+\left (x -y \sqrt {x^{2}+y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
10.000 |
|
| \begin{align*}
y-x^{5} y^{4}+\left (x -x^{4} y^{5}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
5.955 |
|
| \begin{align*}
x^{3}-x y^{2}+y+\left (y^{3}-x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
13.523 |
|
| \begin{align*}
x^{3}+2 x y^{2}-x +\left (x^{2} y+2 y^{3}-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
52.439 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+2 y}{x^{3}+x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.843 |
|
| \begin{align*}
x y^{2}+x \sin \left (x \right )^{2}-\sin \left (2 x \right )-2 y y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
2.657 |
|
| \begin{align*}
x^{2}+y \left (x -y\right )^{2} \tan \left (\frac {y}{x}\right )-\left (x^{2}+x \left (x -y\right )^{2} \tan \left (\frac {y}{x}\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
132.289 |
|
| \begin{align*}
y^{\prime \prime }&=2 x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 10 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.126 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }&=\frac {x}{3} \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.237 |
|
| \begin{align*}
y^{\prime \prime \prime }&=3 \sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= -2 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.255 |
|
| \begin{align*}
2 y^{\prime \prime \prime \prime }&={\mathrm e}^{x}-{\mathrm e}^{-x} \\
y \left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.475 |
|
| \begin{align*}
i^{\prime \prime }&=t^{2}+1 \\
i \left (0\right ) &= 2 \\
i^{\prime }\left (0\right ) &= 3 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.313 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=x^{2}+1 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.333 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }&=1+\sqrt {x} \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
y^{\prime } y^{\prime \prime }&=1 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
1.726 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.884 |
|
| \begin{align*}
x y^{\prime \prime }+2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
6.737 |
|
| \begin{align*}
y y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
3.816 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
12.721 |
|
| \begin{align*}
y^{\prime \prime }&=\left (y+1\right ) y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
5.505 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }&=x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.195 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }&=\ln \left (x \right ) \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
y^{\prime \prime }\left (1\right ) &= 0 \\
y^{\prime \prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| \begin{align*}
y^{\left (5\right )}+2 y^{\prime \prime \prime \prime }&=x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
x y^{\prime \prime \prime }+y^{\prime \prime }&=1 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.150 |
|
| \begin{align*}
{y^{\prime \prime \prime }}^{2}&={y^{\prime \prime }}^{3} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✓ |
✓ |
2.356 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.122 |
|
| \begin{align*}
1+{y^{\prime }}^{2}+y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
7.707 |
|
| \begin{align*}
2 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=1 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.156 |
|
| \begin{align*}
y^{\prime \prime }&=-\frac {4}{y^{3}} \\
y \left (2\right ) &= 4 \\
y^{\prime }\left (2\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✗ |
✓ |
✗ |
1.173 |
|
| \begin{align*}
y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
17.954 |
|