| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x&=\ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.082 |
|
| \begin{align*}
x&={y^{\prime }}^{2}-2 y^{\prime }+2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \begin{align*}
y&=y^{\prime } \ln \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.514 |
|
| \begin{align*}
y&=\left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
x {y^{\prime }}^{2}&={\mathrm e}^{\frac {1}{y^{\prime }}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.318 |
|
| \begin{align*}
x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \begin{align*}
y^{{2}/{5}}+{y^{\prime }}^{{2}/{5}}&=a^{{2}/{5}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.434 |
|
| \begin{align*}
x&=\sin \left (y^{\prime }\right )+y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.154 |
|
| \begin{align*}
y&=y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.871 |
|
| \begin{align*}
y&=\arcsin \left (y^{\prime }\right )+\ln \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.650 |
|
| \begin{align*}
y&=2 y^{\prime } x +\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.576 |
|
| \begin{align*}
y&=x \left (1+y^{\prime }\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \begin{align*}
y&=2 y^{\prime } x +\sin \left (y^{\prime }\right ) \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.607 |
|
| \begin{align*}
y&=x {y^{\prime }}^{2}-\frac {1}{y^{\prime }} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
116.778 |
|
| \begin{align*}
y&=\frac {3 y^{\prime } x}{2}+{\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.057 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {a}{{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.523 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| \begin{align*}
x {y^{\prime }}^{2}-y y^{\prime }-y^{\prime }+1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.212 |
|
| \begin{align*}
y&=y^{\prime } x +a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.935 |
|
| \begin{align*}
x&=\frac {y}{y^{\prime }}+\frac {1}{{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.467 |
|
| \begin{align*}
{\mathrm e}^{-x} y^{\prime }+y^{2}-2 \,{\mathrm e}^{x} y&=1-{\mathrm e}^{2 x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
168.464 |
|
| \begin{align*}
y^{\prime }+y^{2}-2 \sin \left (x \right ) y+\sin \left (x \right )^{2}-\cos \left (x \right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
y^{\prime } x -y^{2}+\left (2 x +1\right ) y&=x^{2}+2 x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.868 |
|
| \begin{align*}
x^{2} y^{\prime }&=1+y x +y^{2} x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.884 |
|
| \begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )-4 y y^{\prime }-4 x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.386 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.504 |
|
| \begin{align*}
{y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
0.398 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.175 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}}+a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.250 |
|
| \begin{align*}
\left (y^{\prime } x +y\right )^{2}+3 x^{5} \left (y^{\prime } x -2 y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
0.651 |
|
| \begin{align*}
y \left (y-2 y^{\prime } x \right )^{2}&=2 y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \begin{align*}
8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2}&=-27 x +27 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
0.516 |
|
| \begin{align*}
\left (y^{\prime }-1\right )^{2}&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.220 |
|
| \begin{align*}
y&={y^{\prime }}^{2}-y^{\prime } x +x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.612 |
|
| \begin{align*}
\left (y^{\prime } x +y\right )^{2}&=y^{2} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
46.470 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+y^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.270 |
|
| \begin{align*}
{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.234 |
|
| \begin{align*}
3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| \begin{align*}
y&=y^{\prime } x +\sqrt {a^{2} {y^{\prime }}^{2}+b^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.154 |
|
| \begin{align*}
y^{\prime }&=\left (x -y\right )^{2}+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.077 |
|
| \begin{align*}
x \sin \left (x \right ) y^{\prime }+\left (-\cos \left (x \right ) x +\sin \left (x \right )\right ) y&=\cos \left (x \right ) \sin \left (x \right )-x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.076 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.806 |
|
| \begin{align*}
x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
57.199 |
|
| \begin{align*}
5 y x -4 y^{2}-6 x^{2}+\left (y^{2}-8 y x +\frac {5 x^{2}}{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.635 |
|
| \begin{align*}
3 x y^{2}-x^{2}+\left (3 x^{2} y-6 y^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
1.712 |
|
| \begin{align*}
y-x y^{2} \ln \left (x \right )+y^{\prime } x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.599 |
|
| \begin{align*}
2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.190 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{2 x -y^{2}} \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.346 |
|
| \begin{align*}
x^{2}+y^{\prime } x&=3 x +y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| \begin{align*}
y y^{\prime } x -y^{2}&=x^{4} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.170 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
18.619 |
|
| \begin{align*}
\left (2 x -1\right ) y^{\prime }-2 y&=\frac {1-4 x}{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.569 |
|
| \begin{align*}
x -y+3+\left (3 x +y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.344 |
|
| \begin{align*}
y^{\prime }+\cos \left (\frac {x}{2}+\frac {y}{2}\right )&=\cos \left (\frac {x}{2}-\frac {y}{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.260 |
|
| \begin{align*}
y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.860 |
|
| \begin{align*}
y^{2} y^{\prime } x -y^{3}&=\frac {x^{4}}{3} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.836 |
|
| \begin{align*}
1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.725 |
|
| \begin{align*}
x^{2}+y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.799 |
|
| \begin{align*}
x -y+2+\left (x -y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.455 |
|
| \begin{align*}
y+x y^{2}-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.517 |
|
| \begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.795 |
|
| \begin{align*}
\left (x -1\right ) \left (y^{2}-y+1\right )&=\left (-1+y\right ) \left (x^{2}+x +1\right ) y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.128 |
|
| \begin{align*}
\left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
2.165 |
|
| \begin{align*}
\cos \left (x \right ) y+\left (2 y-\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.885 |
|
| \begin{align*}
y^{\prime }-1&={\mathrm e}^{x +2 y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| \begin{align*}
2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
3.246 |
|
| \begin{align*}
x^{2} y^{n} y^{\prime }&=2 y^{\prime } x -y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
3.009 |
|
| \begin{align*}
\left (3 x +3 y+a^{2}\right ) y^{\prime }&=4 x +4 y+b^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.122 |
|
| \begin{align*}
x -y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.086 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.693 |
|
| \begin{align*}
\sin \left (\ln \left (x \right )\right )-\cos \left (\ln \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.522 |
|
| \begin{align*}
y^{\prime }&=\sqrt {\frac {9 y^{2}-6 y+2}{x^{2}-2 x +5}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.979 |
|
| \begin{align*}
\left (5 x -7 y+1\right ) y^{\prime }+x +y-1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
113.291 |
|
| \begin{align*}
x +y+1+\left (2 x +2 y-1\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.673 |
|
| \begin{align*}
y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
3.007 |
|
| \begin{align*}
y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
2.874 |
|
| \begin{align*}
4 x^{2} {y^{\prime }}^{2}-y^{2}&=x y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
1.228 |
|
| \begin{align*}
y^{\prime }+x {y^{\prime }}^{2}-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.069 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 \cos \left (x \right )+2 \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \begin{align*}
x y^{\prime \prime \prime }&=2 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.133 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.265 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
{y^{\prime }}^{4}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.652 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.215 |
|
| \begin{align*}
y^{\prime \prime }&=\left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
2.104 |
|
| \begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.056 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }&=x \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.083 |
|
| \begin{align*}
y^{\prime \prime \prime }&=x +\cos \left (x \right ) \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.111 |
|
| \begin{align*}
y^{\prime \prime } \left (2+x \right )^{5}&=1 \\
y \left (-1\right ) &= {\frac {1}{12}} \\
y^{\prime }\left (-1\right ) &= -{\frac {1}{4}} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| \begin{align*}
y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.681 |
|
| \begin{align*}
y^{\prime \prime }&=2 x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \begin{align*}
y^{\prime \prime } x&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \begin{align*}
y^{\prime \prime } x&=\left (2 x^{2}+1\right ) y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
y^{\prime \prime } x&=y^{\prime }+x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.589 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.237 |
|
| \begin{align*}
y x&=y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.164 |
|
| \begin{align*}
2 y^{\prime \prime }&=\frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }} \\
y \left (1\right ) &= \frac {\sqrt {2}}{5} \\
y^{\prime }\left (1\right ) &= \frac {\sqrt {2}}{2} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
y^{\prime \prime \prime }&=\sqrt {1-{y^{\prime \prime }}^{2}} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✗ |
✓ |
✓ |
0.842 |
|