| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2}+y^{2}-2 y y^{\prime } x&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.959 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x -2 y^{2}-\left (x^{2}-3 y x \right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
3.145 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y-\left (x -y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-3 x y^{2}-y^{\prime } x&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.577 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+x \left (x^{2} y-1\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
1.793 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+x^{3} y+2 x^{2}+\left (x +4 y^{4} x +8 y^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[_rational] |
✓ |
✓ |
✓ |
✗ |
1.114 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y-{\mathrm e}^{x} x^{2}+y^{\prime } x&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.841 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 1+y^{2}&=\left (x^{2}+x \right ) y^{\prime } \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.219 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-x^{3}+y^{\prime } x&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.277 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+\left (y^{2}-x \right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.618 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{3}-y x -\left (x^{2}+6 x y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
1.323 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{2} x^{2}+4 \left (x^{3} y-3\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
1.072 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (x +y\right )-x^{2} y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.606 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (y^{2}-2 x^{2}\right )+x \left (2 y^{2}-x^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.490 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime } x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.250 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&=2 x +2 \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.393 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-y&=y x \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.986 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -3 y-\left (x -2\right ) {\mathrm e}^{x}+y^{\prime } x&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.018 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} i^{\prime }-6 i&=10 \sin \left (2 t \right ) \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.208 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&=y^{2} {\mathrm e}^{x} \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.852 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+\left (y x +x -3 y\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
5.776 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime }&=2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right ) \end {array} \]
|
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
17.599 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +y-x^{3} y^{6}&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.190 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} r^{\prime }+2 r \cos \left (\theta \right )+\sin \left (2 \theta \right )&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.217 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (1+y^{2}\right )&=2 \left (1-2 x y^{2}\right ) y^{\prime } \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.502 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime }-x y^{2}+x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.621 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y&=0 \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
4.380 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{\prime }-\frac {x}{y}+x^{3} \cos \left (y \right )&=0 \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.000 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=y \left (1-x \tan \left (x \right )\right )+x^{2} \cos \left (x \right ) \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
26.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2+y^{2}-\left (y x +2 y+y^{3}\right ) y^{\prime }&=0 \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
14.448 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 1+y^{2}&=\left (\arctan \left (y\right )-x \right ) y^{\prime } \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.606 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{5}-y+2 y^{\prime } x&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.168 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 1+\sin \left (y\right )&=\left (2 y \cos \left (y\right )-x \left (\sec \left (y\right )+\tan \left (y\right )\right )\right ) y^{\prime } \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
8.953 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=2 y+{\mathrm e}^{x} x^{3}\\ y \left (1\right )&=0\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.787 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} L i^{\prime }+R i&=E \sin \left (2 t \right )\\ i \left (0\right )&=0\\ \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.878 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \cos \left (y\right ) y^{\prime }&=2 x \sin \left (y\right )-1 \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
5.542 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y y^{\prime }&=3 x \left (3 y^{2}+2\right )+2 \left (3 y^{2}+2\right )^{3} \end {array} \]
|
[_rational] |
✓ |
✓ |
✓ |
✓ |
27.955 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{3}-y^{3}-{\mathrm e}^{x} x^{2}+3 y^{2} y^{\prime } x&=0 \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.576 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+x \left (x +y\right )&=x^{3} \left (x +y\right )^{3}-1 \end {array} \]
|
[_Abel] |
✓ |
✓ |
✓ |
✓ |
5.428 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+{\mathrm e}^{y}-{\mathrm e}^{-x}+\left (1+{\mathrm e}^{y}\right ) y^{\prime }&=0 \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
4.114 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}+y y^{\prime } x -6 y^{2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+\left (y-1-x^{2}\right ) y^{\prime }-\left (-1+y\right ) x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.132 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.143 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{4} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.865 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 8 y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.770 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
2.630 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-y^{\prime } x +y&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.397 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 16 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
1.577 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{5}-y {y^{\prime }}^{4}+\left (x^{2}+1\right ) {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime }-y&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.336 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-y y^{\prime }-y&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.752 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.506 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.873 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=x \left (1+y^{\prime }\right )+{y^{\prime }}^{2} \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
148.123 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=2 y^{\prime }+\sqrt {1+{y^{\prime }}^{2}} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.805 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime }}^{2}-y^{\prime } x +3 y&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.250 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=y^{\prime } x -2 {y^{\prime }}^{2} \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} {y^{\prime }}^{2}+3 y^{\prime } x -y&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
1.925 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.321 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.435 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (3 y-1\right )^{2} {y^{\prime }}^{2}&=4 y \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
87.997 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=-y^{\prime } x +x^{4} {y^{\prime }}^{2} \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.573 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y&={y^{\prime }}^{2}+4 y^{\prime } x \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.232 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (3-4 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
1.383 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1+{y^{\prime }}^{2}\right ) \left (x -y\right )^{2}&=\left (x +y y^{\prime }\right )^{2} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
31.186 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-6 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.156 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{5 x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.944 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=\cos \left (x \right ) x \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.209 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.114 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=3 x^{4} \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.270 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.134 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \end {array} \]
|
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
2.135 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime \prime }+{y^{\prime }}^{2}&=2 \end {array} \]
|
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
2.478 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}+y y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
0.438 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-15 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.843 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.176 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+12 y^{\prime \prime }-8 y^{\prime }&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.048 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.902 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+25 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.587 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime }+9 y^{\prime }-9 y&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.040 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.066 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+3 y&=1 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.230 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }&=5 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.973 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-4 y^{\prime \prime }&=5 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.084 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (5\right )}-4 y^{\prime \prime \prime }&=5 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -4 y^{\prime }+y^{\prime \prime \prime }&=x \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.088 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.025 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&=-2 x^{2}+2 x +2 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.044 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=4 x \,{\mathrm e}^{x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.092 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\sin \left (x \right )^{2} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.145 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.457 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\csc \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.165 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-3 y^{\prime }+y^{\prime \prime }&=\sin \left ({\mathrm e}^{-x}\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.224 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\csc \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.110 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+y^{\prime \prime }&=4 \sec \left (x \right )^{2} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.316 |
|