| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
12.322 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y^{2} x^{2}-1\right ) y^{\prime }+2 x y^{3}&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
22.439 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right )&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
28.831 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \end {array} \]
|
[_rational] |
✓ |
✓ |
✓ |
✗ |
81.728 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 y x -x^{3}+x \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.292 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-x y^{2} \ln \left (x \right )+y^{\prime } x&=0 \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.439 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3}&=0 \end {array} \]
|
[_rational] |
✗ |
✓ |
✓ |
✗ |
14.360 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.070 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x +y^{2}&=y^{2} x^{2}+x^{4} \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
18.473 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.930 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.516 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3} x&=1+y^{\prime } \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.645 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}-x^{3} \left (1-y^{\prime }\right )&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
79.668 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{3}+y^{3}-3 y y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
84.653 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.683 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} \left (y^{\prime }-1\right )&=\left (2-y^{\prime }\right )^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.747 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \left (1+{y^{\prime }}^{2}\right )&=2 \alpha \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.179 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{4}&=4 y \left (y^{\prime } x -2 y\right )^{2} \end {array} \]
|
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
354.688 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=2 y^{\prime } x +\frac {x^{2}}{2}+{y^{\prime }}^{2} \end {array} \]
|
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
6.215 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=\frac {k \left (x +y y^{\prime }\right )}{\sqrt {1+{y^{\prime }}^{2}}} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✗ |
9.576 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x&=y y^{\prime }+a {y^{\prime }}^{2} \end {array} \]
|
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.439 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=x {y^{\prime }}^{2}+{y^{\prime }}^{3} \end {array} \]
|
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
13.305 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{2} \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
1.071 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=2 y^{\prime } x +y^{2} {y^{\prime }}^{3} \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
36.315 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2} \left (x^{2}-1\right )-2 y y^{\prime } x +y^{2}-1&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.424 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}+2 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
38.196 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {y-x} \end {array} \]
|
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.748 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {y-x}+1 \end {array} \]
|
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.570 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {y} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.081 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\ln \left (y\right ) y \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.326 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y \ln \left (y\right )^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.017 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-x +\sqrt {x^{2}+2 y} \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
11.746 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-x -\sqrt {x^{2}+2 y} \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
11.623 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.133 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.600 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} \left (y^{\prime }-1\right )&=\left (2-y^{\prime }\right )^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.559 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{4}&=4 y \left (y^{\prime } x -2 y\right )^{2} \end {array} \]
|
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
347.605 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x +2 y x&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.639 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&={y^{\prime }}^{2}-y^{\prime } x +\frac {x^{3}}{2} \end {array} \]
|
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
48.484 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=2 y^{\prime } x +\frac {x^{2}}{2}+{y^{\prime }}^{2} \end {array} \]
|
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
6.734 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.983 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime \prime }}^{2}+x^{2}&=1 \end {array} \]
|
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
3.700 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {1}{\sqrt {y}} \end {array} \]
|
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
13.529 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a^{3} y^{\prime \prime \prime } y^{\prime \prime }&=\sqrt {1+c^{2} {y^{\prime \prime }}^{2}} \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✓ |
✗ |
2.771 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }&=\sqrt {1+{y^{\prime \prime }}^{2}} \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✓ |
✓ |
2.380 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \left (2 a -y\right ) y^{\prime \prime }&=1+{y^{\prime }}^{2} \end {array} \]
|
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
4.281 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x y^{\prime \prime \prime }+{y^{\prime \prime \prime }}^{3}&=0 \end {array} \]
|
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
5.621 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime \prime }+{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2} \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
8.597 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \end {array} \]
|
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.064 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime }&=0 \end {array} \]
|
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.096 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} n \,x^{3} y^{\prime \prime }&=\left (y-y^{\prime } x \right )^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
2.055 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} \left (x^{2} y^{\prime \prime }-y^{\prime } x +y\right )&=x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
1.597 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{2} y^{\prime \prime }-3 y^{2} y^{\prime } x +4 y^{3}+x^{6}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
1.439 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2}&=0 \end {array} \]
|
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✗ |
✗ |
✗ |
✗ |
101.730 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2} y^{\prime }+2 y x \right ) y^{\prime \prime }+4 x {y^{\prime }}^{2}+8 y y^{\prime } x +4 y^{2}-1&=0 \end {array} \]
|
[NONE] |
✗ |
✗ |
✗ |
✗ |
8.574 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (y x +1\right ) y^{\prime \prime }+x^{2} {y^{\prime }}^{2}+\left (4 y x +2\right ) y^{\prime }+y^{2}+1&=0 \end {array} \]
|
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.354 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a^{2} y^{\prime \prime }&=2 x \sqrt {1+{y^{\prime }}^{2}} \end {array} \]
|
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✗ |
✓ |
✗ |
0.673 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y y^{\prime \prime }+x^{2} {y^{\prime }}^{2}-5 y y^{\prime } x&=4 y^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
1.465 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.677 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=0 \end {array} \]
|
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
2.398 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )}&=0 \end {array} \]
|
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.488 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime }}^{2}+2 y^{\prime \prime } x -y^{\prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
9.611 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime }}^{2}-2 y^{\prime \prime } x -y^{\prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.265 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+12 y^{\prime } x -12 y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.280 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-\frac {3 y^{\prime \prime }}{x}+\frac {6 y^{\prime }}{x^{2}}-\frac {6 y}{x^{3}}&=0 \end {array} \]
|
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \]
|
[_Gegenbauer] |
✗ |
✓ |
✓ |
✗ |
109.759 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+y&=0 \end {array} \]
|
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right )^{2} y^{\prime \prime }&=2 y \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.985 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.271 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.110 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime \prime }-y^{\prime \prime } x +y^{\prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.398 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=2 x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.287 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {x y^{\prime }}{1-x}-\frac {y}{1-x}&=-1+x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.300 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y x +\left (x^{2}+2\right ) y^{\prime }-2 y^{\prime \prime } x +\left (x^{2}+2\right ) y^{\prime \prime \prime }&=x^{4}+12 \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
0.146 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.076 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.768 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y}{x^{2} \ln \left (x \right )}&={\mathrm e}^{x} \left (\frac {2}{x}+\ln \left (x \right )\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
5.429 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+p_{1} y^{\prime }+p_{2} y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.358 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.120 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right )^{2} y^{\prime \prime }+\cos \left (x \right ) \sin \left (x \right ) y^{\prime }&=y \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.103 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.110 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+4 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.087 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.083 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+y^{\prime }-y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.169 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=x^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.577 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{x}+{\mathrm e}^{2 x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=x \,{\mathrm e}^{x} \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.210 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{x} \left (x +1\right ) \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.299 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+y^{\prime \prime }&=\sin \left (2 x \right ) x \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.883 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\frac {{\mathrm e}^{x}-{\mathrm e}^{-x}}{{\mathrm e}^{x}+{\mathrm e}^{-x}} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y&=4 x^{2} {\mathrm e}^{x^{2}} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (2 x \right ) \sin \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.656 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=\ln \left (2 \sin \left (\frac {x}{2}\right )\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.014 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {n \left (n +1\right ) y}{x^{2}}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.747 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.356 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.874 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y&=x^{2}+\frac {1}{x} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.254 |
|