| # | ID | ODE | CAS classification |
Maple |
Mma |
Sympy |
time(sec) |
| \(1\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.059 |
|
| \(2\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }+t y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.053 |
|
| \(3\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2-t \right ) y^{\prime \prime \prime }+\left (2 t -3\right ) y^{\prime \prime }-y^{\prime } t +y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.058 |
|
| \(4\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} \left (t +3\right ) y^{\prime \prime \prime }-3 t \left (t +2\right ) y^{\prime \prime }+6 \left (1+t \right ) y^{\prime }-6 y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.059 |
|
| \(5\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y y^{\prime \prime \prime }+2 \left (y+3 y^{\prime }\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}&=\sin \left (x \right ) \end {array} \]
|
[[_3rd_order, _exact, _nonlinear]] |
✓ |
✓ |
✗ |
0.035 |
|
| \(6\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }&=y x \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.027 |
|
| \(7\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2 y^{\prime } x +y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.033 |
|
| \(8\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y+2 a x y^{\prime }+y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.035 |
|
| \(9\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y f^{\prime }\left (x \right )+2 f \left (x \right ) y^{\prime }+y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.046 |
|
| \(10\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -8 a x y-2 \left (-4 x^{2}-2 a +1\right ) y^{\prime }-6 y^{\prime \prime } x +y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.055 |
|
| \(11\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a^{3} x^{3} y+3 a^{2} x^{2} y^{\prime }+3 a x y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.046 |
|
| \(12\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.039 |
|
| \(13\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y^{\prime }+\left (2 \cot \left (x \right )+\csc \left (x \right )\right ) y^{\prime \prime }+y^{\prime \prime \prime }&=\cot \left (x \right ) \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✗ |
3.711 |
|
| \(14\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y \left (2 f \left (x \right ) g \left (x \right )+g^{\prime }\left (x \right )\right )+\left (4 g \left (x \right )+f^{\prime }\left (x \right )+2 {f^{\prime }\left (x \right )}^{2}\right ) y^{\prime }+3 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.068 |
|
| \(15\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} f \left (x \right ) y+y^{\prime }+f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(16\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x +3 y^{\prime }+x y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.036 |
|
| \(17\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.040 |
|
| \(18\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.041 |
|
| \(19\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=-x^{2}+1 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.044 |
|
| \(20\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -x^{2} y+3 y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.035 |
|
| \(21\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a \,x^{2} y-6 y^{\prime }+x^{2} y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.040 |
|
| \(22\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y x +\left (x^{2}+2\right ) y^{\prime }+4 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=f \left (x \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.048 |
|
| \(23\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a \,x^{2} y+6 y^{\prime }+6 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.045 |
|
| \(24\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{3} y+\left (-2 x^{3}+6\right ) y^{\prime }+x \left (-x^{2}+6\right ) y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.049 |
|
| \(25\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 10 y^{\prime }+8 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✗ |
✗ |
0.618 |
|
| \(26\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y x +\left (x^{2}+2\right ) y^{\prime }-2 y^{\prime \prime } x +\left (x^{2}+2\right ) y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.040 |
|
| \(27\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(28\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime } x +\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime \prime }+x \left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime \prime }&=f \left (x \right ) \end {array} \]
|
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
2.645 |
|
| \(29\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 \left (x^{2}+4\right ) y+x \left (x^{2}+8\right ) y^{\prime }-4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.044 |
|
| \(30\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+2 y^{\prime } x +x^{2} \ln \left (x \right ) y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=2 x^{3} \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
1.515 |
|
| \(31\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -12 y+3 \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.041 |
|
| \(32\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -8 y+3 \left (x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right )^{3} y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(33\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -6 y+6 \left (x +1\right ) y^{\prime }-3 x \left (2+x \right ) y^{\prime \prime }+x^{2} \left (3+y\right ) y^{\prime \prime \prime }&=0 \end {array} \]
|
[NONE] |
✗ |
✗ |
✗ |
0.043 |
|
| \(34\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+\left (1-2 x \right ) y^{\prime }+\left (1-2 x \right )^{3} y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.040 |
|
| \(35\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -4 \left (1+3 x \right ) y+2 x \left (2+5 x \right ) y^{\prime }-2 x^{2} \left (2 x +1\right ) y^{\prime \prime }+x^{3} \left (x +1\right ) y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.049 |
|
| \(36\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -4 \left (3 x^{2}+1\right ) y+2 x \left (5 x^{2}+2\right ) y^{\prime }-2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.049 |
|
| \(37\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a -x \right )^{3} \left (b -x \right )^{3} y^{\prime \prime \prime }&=c y \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.048 |
|
| \(38\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 10 f^{\prime }\left (x \right ) y^{\prime }+3 y \left (3 f \left (x \right )^{2}+f^{\prime \prime }\left (x \right )\right )+10 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.069 |
|
| \(39\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}-2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \end {array} \]
|
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.037 |
|
| \(40\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}-2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x^{3} \end {array} \]
|
[NONE] |
✗ |
✗ |
✗ |
0.040 |
|
| \(41\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a^{4} x^{4} y+4 a^{3} x^{3} y^{\prime }+6 a^{2} x^{2} y^{\prime \prime }+4 a x y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.059 |
|
| \(42\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -a^{2} y+12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(43\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -c^{4} y+16 \left (1+a -b \right ) \left (2+a -b \right ) y^{\prime \prime }+32 \left (2+a -b \right ) x y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime \prime \prime }&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.055 |
|
| \(44\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -a^{4} x^{3} y-y^{\prime \prime } x +2 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.047 |
|
| \(45\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -k y-\left (-a b c +x \right ) y^{\prime }+\left (a b +a c +b c +a +b +c +1\right ) x y^{\prime \prime }+\left (3+a +b +c \right ) x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.057 |
|
| \(46\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -b^{4} x^{\frac {2}{a}} y+16 \left (-2 a +1\right ) \left (1-a \right ) a^{2} x^{2} y^{\prime \prime }-32 \left (-2 a +1\right ) a^{2} x^{3} y^{\prime \prime \prime }+16 a^{4} x^{4} y^{\prime \prime \prime \prime }&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.094 |
|
| \(47\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y y^{\prime }+{y^{\prime }}^{2}+y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.038 |
|
| \(48\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.032 |
|
| \(49\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}-\left (1-2 y x \right ) y^{\prime }+y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=f \left (x \right ) \end {array} \]
|
[[_3rd_order, _exact, _nonlinear]] |
✗ |
✗ |
✗ |
0.045 |
|
| \(50\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-y\right ) y^{\prime }+x {y^{\prime }}^{2}-x \left (1-y\right ) y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✗ |
0.047 |
|
| \(51\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{3} y^{\prime }-y^{\prime } y^{\prime \prime }+y y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.039 |
|
| \(52\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime } y^{\prime \prime }+\left (a +y\right ) y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✗ |
0.037 |
|
| \(53\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{2}+18 y y^{\prime } x +9 x^{2} {y^{\prime }}^{2}+9 x^{2} y y^{\prime \prime }+3 x^{3} y^{\prime } y^{\prime \prime }+x^{3} y y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.053 |
|
| \(54\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 {y^{\prime }}^{3}+3 y^{\prime \prime }+6 y y^{\prime } y^{\prime \prime }+\left (x +y^{2}\right ) y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.049 |
|
| \(55\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(56\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.041 |
|
| \(57\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }&=\left (a +3 y^{\prime }\right ) {y^{\prime \prime }}^{2} \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✗ |
10.522 |
|
| \(58\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )}&=0 \end {array} \]
|
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.147 |
|
| \(59\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 y^{\prime } x -4 y&=8 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.043 |
|
| \(60\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1+2 y+3 y^{2}\right ) y^{\prime \prime \prime }+6 y^{\prime } \left (y^{\prime \prime }+{y^{\prime }}^{2}+3 y y^{\prime \prime }\right )&=x \end {array} \]
|
[[_3rd_order, _exact, _nonlinear]] |
✓ |
✓ |
✗ |
0.053 |
|
| \(61\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x \left (y^{2} y^{\prime \prime \prime }+6 y y^{\prime } y^{\prime \prime }+2 {y^{\prime }}^{3}\right )-3 y \left (y y^{\prime \prime }+2 {y^{\prime }}^{2}\right )&=-\frac {2}{x} \end {array} \]
|
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.059 |
|
| \(62\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime \prime \prime }+3 y^{\prime } y^{\prime \prime }-2 y y^{\prime \prime }-2 {y^{\prime }}^{2}+y y^{\prime }&={\mathrm e}^{2 x} \end {array} \]
|
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.065 |
|
| \(63\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y&=0 \end {array} \]
|
[NONE] |
✗ |
✗ |
✗ |
0.033 |
|
| \(64\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.046 |
|
| \(65\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-2 y^{\prime \prime } x +4 x^{2} y^{\prime }+8 x^{3} y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.046 |
|
| \(66\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y x&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.046 |
|
| \(67\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3}&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.039 |
|
| \(68\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y x&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.033 |
|
| \(69\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y a \,x^{3}-b x&=0 \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.061 |
|
| \(70\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-a \,x^{b} y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.060 |
|
| \(71\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y+2 a x y^{\prime }+y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.057 |
|
| \(72\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+\left (a +b -1\right ) x y^{\prime }-a b y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.076 |
|
| \(73\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+x^{2 c -2} y^{\prime }+\left (c -1\right ) x^{2 c -3} y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.125 |
|
| \(74\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-\left (6 k^{2} \sin \left (x \right )^{2}+a \right ) y^{\prime }+b y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.076 |
|
| \(75\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y f^{\prime }\left (x \right )+2 f \left (x \right ) y^{\prime }+y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.075 |
|
| \(76\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-6 y^{\prime \prime } x +2 \left (4 x^{2}+2 a -1\right ) y^{\prime }-8 a x y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.072 |
|
| \(77\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a^{3} x^{3} y+3 a^{2} x^{2} y^{\prime }+3 a x y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.076 |
|
| \(78\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} f \left (x \right ) y+y^{\prime }+f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.066 |
|
| \(79\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+f \left (x \right ) \left (x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y\right )&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.074 |
|
| \(80\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime \prime }+3 y^{\prime \prime }+y x&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.059 |
|
| \(81\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime \prime }+3 y^{\prime \prime }-a \,x^{2} y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.062 |
|
| \(82\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime \prime }+\left (a +b \right ) y^{\prime \prime }-y^{\prime } x -a y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.065 |
|
| \(83\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime \prime }-\left (x +2 v \right ) y^{\prime \prime }-\left (x -2 v -1\right ) y^{\prime }+\left (-1+x \right ) y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.066 |
|
| \(84\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{\prime \prime \prime }+3 y^{\prime \prime }+a x y-b&=0 \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.060 |
|
| \(85\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{\prime \prime \prime }-4 \left (x +\nu -1\right ) y^{\prime \prime }+\left (2 x +6 \nu -5\right ) y^{\prime }+\left (1-2 \nu \right ) y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.076 |
|
| \(86\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x y^{\prime \prime \prime }+3 \left (2 a x +k \right ) y^{\prime \prime }+6 \left (a k +b x \right ) y^{\prime }+\left (3 b k +2 c x \right ) y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.079 |
|
| \(87\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x -1\right ) y^{\prime \prime \prime }-8 y^{\prime } x +8 y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.060 |
|
| \(88\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a \,x^{2} y-6 y^{\prime }+x^{2} y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.062 |
|
| \(89\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime }+\left (x +1\right ) y^{\prime \prime }-y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.060 |
|
| \(90\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime }-3 \left (x -m \right ) x y^{\prime \prime }+\left (2 x^{2}+4 \left (n -m \right ) x +m \left (2 m -1\right )\right ) y^{\prime }-2 n \left (2 x -2 m +1\right ) y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.097 |
|
| \(91\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime }+4 y^{\prime \prime } x +\left (x^{2}+2\right ) y^{\prime }+3 y x -f \left (x \right )&=0 \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.069 |
|
| \(92\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a \,x^{2} y+6 y^{\prime }+6 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.066 |
|
| \(93\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime }-3 \left (p +q \right ) x y^{\prime \prime }+3 p \left (3 q +1\right ) y^{\prime }-x^{2} y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.066 |
|
| \(94\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime }-2 \left (n +1\right ) x y^{\prime \prime }+\left (a \,x^{2}+6 n \right ) y^{\prime }-2 a x y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.074 |
|
| \(95\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime }-\left (x^{2}-2 x \right ) y^{\prime \prime }-\left (x^{2}+\nu ^{2}-\frac {1}{4}\right ) y^{\prime }+\left (x^{2}-2 x +\nu ^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.076 |
|
| \(96\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime }-\left (x +\nu \right ) x y^{\prime \prime }+\nu \left (2 x +1\right ) y^{\prime }-\nu \left (x +1\right ) y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.077 |
|
| \(97\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime }-2 \left (x^{2}-x \right ) y^{\prime \prime }+\left (x^{2}-2 x +\frac {1}{4}-\nu ^{2}\right ) y^{\prime }+\left (\nu ^{2}-\frac {1}{4}\right ) y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.074 |
|
| \(98\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime }-\left (x^{4}-6 x \right ) y^{\prime \prime }-\left (2 x^{3}-6\right ) y^{\prime }+2 x^{2} y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.068 |
|
| \(99\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y x +\left (x^{2}+2\right ) y^{\prime }-2 y^{\prime \prime } x +\left (x^{2}+2\right ) y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.065 |
|
| \(100\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \left (-1+x \right ) y^{\prime \prime \prime }+3 \left (2 x -1\right ) y^{\prime \prime }+\left (2 a x +b \right ) y^{\prime }+a y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.070 |
|
| \(101\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }+\left (-\nu ^{2}+1\right ) x y^{\prime }+\left (a \,x^{3}+\nu ^{2}-1\right ) y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.070 |
|
| \(102\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }+\left (4 x^{3}+\left (-4 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (4 \nu ^{2}-1\right ) y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.067 |
|
| \(103\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }+\left (a \,x^{2 \nu }+1-\nu ^{2}\right ) x y^{\prime }+\left (b \,x^{3 \nu }+a \left (\nu -1\right ) x^{2 \nu }+\nu ^{2}-1\right ) y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.163 |
|
| \(104\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 \left (x^{2}+4\right ) y+x \left (x^{2}+8\right ) y^{\prime }-4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.072 |
|
| \(105\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }+3 \left (1-a \right ) x^{2} y^{\prime \prime }+\left (4 b^{2} c^{2} x^{2 c +1}+1-4 \nu ^{2} c^{2}+3 a \left (-1+a \right ) x \right ) y^{\prime }+\left (4 b^{2} c^{2} \left (c -a \right ) x^{2 c}+a \left (4 \nu ^{2} c^{2}-a^{2}\right )\right ) y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.099 |
|
| \(106\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }+\left (x +3\right ) x^{2} y^{\prime \prime }+5 \left (x -6\right ) x y^{\prime }+\left (4 x +30\right ) y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.069 |
|
| \(107\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -12 y+3 \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.063 |
|
| \(108\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +3\right ) x^{2} y^{\prime \prime \prime }-3 x \left (2+x \right ) y^{\prime \prime }+6 \left (x +1\right ) y^{\prime }-6 y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.067 |
|
| \(109\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \left (x -\operatorname {a1} \right ) \left (x -\operatorname {a2} \right ) \left (x -\operatorname {a3} \right ) y^{\prime \prime \prime }+\left (9 x^{2}-6 \left (\operatorname {a1} +\operatorname {a2} +\operatorname {a3} \right ) x +3 \operatorname {a1} \operatorname {a2} +3 \operatorname {a3} \operatorname {a1} +3 \operatorname {a2} \operatorname {a3} \right ) y^{\prime \prime }-2 \left (\left (n^{2}+n -3\right ) x +b \right ) y^{\prime }-n \left (n +1\right ) y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.080 |
|
| \(110\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} \left (x +1\right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-4 \left (1+3 x \right ) y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.075 |
|
| \(111\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-4 \left (3 x^{2}+1\right ) y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.076 |
|
| \(112\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{6} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.063 |
|
| \(113\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{6} y^{\prime \prime \prime }+6 x^{5} y^{\prime \prime }+a y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.059 |
|
| \(114\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{4}+2 x^{2}+2 x +1\right ) y^{\prime \prime \prime }-\left (2 x^{6}+3 x^{4}-6 x^{2}-6 x -1\right ) y^{\prime \prime }+\left (x^{6}-6 x^{3}-15 x^{2}-12 x -2\right ) y^{\prime }+\left (x^{4}+4 x^{3}+8 x^{2}+6 x +1\right ) y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.083 |
|
| \(115\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -a \right )^{3} \left (x -b \right )^{3} y^{\prime \prime \prime }-c y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.070 |
|
| \(116\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime } \sin \left (x \right )^{2}+3 y^{\prime \prime } \sin \left (x \right ) \cos \left (x \right )+\left (\cos \left (2 x \right )+4 \nu \left (\nu +1\right ) \sin \left (x \right )^{2}\right ) y^{\prime }+2 \nu \left (\nu +1\right ) y \sin \left (2 x \right )&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.091 |
|
| \(117\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime } x +n y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.056 |
|
| \(118\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime } x -n y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.056 |
|
| \(119\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+a \left (b x -1\right ) y^{\prime \prime }+a b y^{\prime }+\lambda y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.076 |
|
| \(120\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+\left (a \,x^{2}+b \lambda +c \right ) y^{\prime \prime }+\left (a \,x^{2}+\beta \lambda +\gamma \right ) y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.082 |
|
| \(121\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a^{4} x^{4} y+4 a^{3} x^{3} y^{\prime }+6 a^{2} x^{2} y^{\prime \prime }+4 a x y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.099 |
|
| \(122\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime } x -\left (6 x^{2}+1\right ) y^{\prime \prime \prime }+12 x^{3} y^{\prime \prime }-\left (9 x^{2}-7\right ) x^{2} y^{\prime }+2 \left (x^{2}-3\right ) x^{3} y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.100 |
|
| \(123\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime \prime }-2 \left (\nu ^{2} x^{2}+6\right ) y^{\prime \prime }+\nu ^{2} \left (\nu ^{2} x^{2}+4\right ) y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.080 |
|
| \(124\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime \prime }+2 x y^{\prime \prime \prime }+a y-b \,x^{2}&=0 \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
✗ |
0.081 |
|
| \(125\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime \prime }+6 x y^{\prime \prime \prime }+6 y^{\prime \prime }-\lambda ^{2} y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.075 |
|
| \(126\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime }-\lambda ^{2} y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.076 |
|
| \(127\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime \prime }+\left (2 n -2 \nu +4\right ) x y^{\prime \prime \prime }+\left (n -\nu +1\right ) \left (n -\nu +2\right ) y^{\prime \prime }-\frac {b^{4} y}{16}&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.089 |
|
| \(128\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime \prime }+2 x^{2} y^{\prime \prime \prime }-y^{\prime \prime } x +y^{\prime }-a^{4} x^{3} y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.080 |
|
| \(129\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime \prime }-2 n \left (n +1\right ) x^{2} y^{\prime \prime }+4 n \left (n +1\right ) x y^{\prime }+\left (a \,x^{4}+n \left (n +1\right ) \left (n +3\right ) \left (-2+n \right )\right ) y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.092 |
|
| \(130\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }+\left (4 n^{2}-1\right ) x y^{\prime }-4 x^{4} y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.186 |
|
| \(131\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }-\left (4 n^{2}-1\right ) x y^{\prime }+\left (-4 x^{4}+4 n^{2}-1\right ) y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.089 |
|
| \(132\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}+3\right ) x^{2} y^{\prime \prime }+\left (12 n^{2}-3\right ) x y^{\prime }-\left (4 x^{4}+12 n^{2}-3\right ) y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.095 |
|
| \(133\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-\rho ^{2}-\sigma ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-\rho ^{2}-\sigma ^{2}+1\right ) x \right ) y^{\prime }+\left (\rho ^{2} \sigma ^{2}+8 x^{2}\right ) y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.098 |
|
| \(134\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-2 \mu ^{2}-2 \nu ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-2 \mu ^{2}-2 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (8 x^{2}+\left (\mu ^{2}-\nu ^{2}\right )^{2}\right ) y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.097 |
|
| \(135\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a \right ) x^{3} y^{\prime \prime \prime }+\left (4 b^{2} c^{2} x^{2 c}+6 \left (-1+a \right )^{2}-2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )+1\right ) x^{2} y^{\prime \prime }+\left (4 \left (3 c -2 a +1\right ) b^{2} c^{2} x^{2 c}+\left (2 a -1\right ) \left (2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )-2 a \left (-1+a \right )-1\right )\right ) x y^{\prime }+\left (4 \left (a -c \right ) \left (a -2 c \right ) b^{2} c^{2} x^{2 c}+\left (c \mu +c \nu +a \right ) \left (c \mu +c \nu -a \right ) \left (c \mu -c \nu +a \right ) \left (c \mu -c \nu -a \right )\right ) y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.146 |
|
| \(136\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a -4 c \right ) x^{3} y^{\prime \prime \prime }+\left (-2 \nu ^{2} c^{2}+2 a^{2}+4 \left (a +c -1\right )^{2}+4 \left (-1+a \right ) \left (c -1\right )-1\right ) x^{2} y^{\prime \prime }+\left (2 \nu ^{2} c^{2}-2 a^{2}-\left (2 a -1\right ) \left (2 c -1\right )\right ) \left (2 a +2 c -1\right ) x y^{\prime }+\left (\left (-\nu ^{2} c^{2}+a^{2}\right ) \left (-\nu ^{2} c^{2}+a^{2}+4 a c +4 c^{2}\right )-b^{4} c^{4} x^{4 c}\right ) y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.129 |
|
| \(137\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \nu ^{4} x^{4} y^{\prime \prime \prime \prime }+\left (4 \nu -2\right ) \nu ^{3} x^{3} y^{\prime \prime \prime }+\left (\nu -1\right ) \left (2 \nu -1\right ) \nu ^{2} x^{2} y^{\prime \prime }-\frac {b^{4} x^{\frac {2}{\nu }} y}{16}&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.114 |
|
| \(138\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right )^{2} y^{\prime \prime \prime \prime }+10 x \left (x^{2}-1\right ) y^{\prime \prime \prime }+\left (24 x^{2}-8-2 \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )\right ) \left (x^{2}-1\right )\right ) y^{\prime \prime }-6 x \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )-2\right ) y^{\prime }+\left (\left (\mu \left (\mu +1\right )-\nu \left (\nu +1\right )\right )^{2}-2 \mu \left (\mu +1\right )-2 \nu \left (\nu +1\right )\right ) y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.106 |
|
| \(139\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime } \sin \left (x \right )^{4}+2 y^{\prime \prime \prime } \sin \left (x \right )^{3} \cos \left (x \right )+y^{\prime \prime } \sin \left (x \right )^{2} \left (\sin \left (x \right )^{2}-3\right )+y^{\prime } \sin \left (x \right ) \cos \left (x \right ) \left (2 \sin \left (x \right )^{2}+3\right )+\left (a^{4} \sin \left (x \right )^{4}-3\right ) y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.114 |
|
| \(140\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime } \sin \left (x \right )^{6}+4 y^{\prime \prime \prime } \sin \left (x \right )^{5} \cos \left (x \right )-6 y^{\prime \prime } \sin \left (x \right )^{6}-4 y^{\prime } \sin \left (x \right )^{5} \cos \left (x \right )+y \sin \left (x \right )^{6}-f&=0 \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.106 |
|
| \(141\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y-\lambda \left (a x -b \right ) \left (y^{\prime \prime }-a^{2} y\right )&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.099 |
|
| \(142\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (5\right )}-a x y-b&=0 \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.077 |
|
| \(143\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (5\right )}+a \,x^{\nu } y^{\prime }+a \nu \,x^{\nu -1} y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.144 |
|
| \(144\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\left (5\right )}-m n y^{\prime \prime \prime \prime }+a x y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.082 |
|
| \(145\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\left (5\right )}-\left (a A_{1} -A_{0} \right ) x -A_{1} -\left (\left (a A_{2} -A_{1} \right ) x +A_{2} \right ) y^{\prime }&=0 \end {array} \]
|
[[_high_order, _missing_y]] |
✗ |
✗ |
✗ |
0.181 |
|
| \(146\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime \prime }-a y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.068 |
|
| \(147\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{10} y^{\left (5\right )}-a y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.083 |
|
| \(148\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{{5}/{2}} y^{\left (5\right )}-a y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.090 |
|
| \(149\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -a \right )^{5} \left (x -b \right )^{5} y^{\left (5\right )}-c y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.100 |
|
| \(150\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y y^{\prime \prime }-{y^{\prime }}^{2}+1&=0 \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.060 |
|
| \(151\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.062 |
|
| \(152\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.060 |
|
| \(153\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime }+y^{\prime \prime } x +\left (2 y x -1\right ) y^{\prime }+y^{2}-f \left (x \right )&=0 \end {array} \]
|
[[_3rd_order, _exact, _nonlinear]] |
✗ |
✗ |
✗ |
0.069 |
|
| \(154\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime }+x \left (-1+y\right ) y^{\prime \prime }+x {y^{\prime }}^{2}+\left (1-y\right ) y^{\prime }&=0 \end {array} \]
|
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✗ |
0.082 |
|
| \(155\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{3} y^{\prime }-y^{\prime } y^{\prime \prime }+y y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.073 |
|
| \(156\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.072 |
|
| \(157\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.069 |
|
| \(158\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } y^{\prime \prime \prime \prime }-y^{\prime \prime } y^{\prime \prime \prime }+{y^{\prime }}^{3} y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.156 |
|
| \(159\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 {y^{\prime \prime }}^{2} y^{\left (5\right )}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+40 y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.251 |
|
| \(160\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }&=f \left (y\right ) \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.053 |
|
| \(161\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.099 |
|
| \(162\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=-x^{2}+1 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.102 |
|
| \(163\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 x^{2} {y^{\prime }}^{2}+36 y y^{\prime } x +6 y^{2}&=0 \end {array} \]
|
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.111 |
|
| \(164\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime }-5 y^{\prime \prime } x +\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.106 |
|
| \(165\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{3} x^{\prime \prime \prime }-\left (t +3\right ) t^{2} x^{\prime \prime }+2 t \left (t +3\right ) x^{\prime }-2 \left (t +3\right ) x&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.115 |
|
| \(166\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y x&=\sin \left (x \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.097 |
|
| \(167\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y y^{\prime \prime \prime \prime }&=1 \end {array} \]
|
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.116 |
|
| \(168\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y x&=\cosh \left (x \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.099 |
|
| \(169\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y x&=\cosh \left (x \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.094 |
|
| \(170\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime \prime } x -y^{2}&=\sin \left (x \right ) \end {array} \]
|
[NONE] |
✗ |
✗ |
✗ |
0.104 |
|
| \(171\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime }&=1 \end {array} \]
|
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.117 |
|
| \(172\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime \prime }}^{2}+\sqrt {y}&=\sin \left (x \right ) \end {array} \]
|
[NONE] |
✗ |
✗ |
✗ |
0.097 |
|
| \(173\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }&=y \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.105 |
|
| \(174\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.109 |
|
| \(175\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }&=3 y y^{\prime }\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&={\frac {3}{2}}\\ \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✗ |
✗ |
0.147 |
|
| \(176\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y&=\cos \left (t \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.136 |
|
| \(177\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.148 |
|
| \(178\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+t y^{\prime \prime }+t^{2} y^{\prime }+t^{2} y&=\ln \left (t \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.149 |
|
| \(179\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -4\right ) y^{\prime \prime \prime \prime }+\left (x +1\right ) y^{\prime \prime }+\tan \left (x \right ) y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.158 |
|
| \(180\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-2\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+3 y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.211 |
|
| \(181\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y&=\cos \left (t \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.119 |
|
| \(182\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.179 |
|
| \(183\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 t^{3} y&=\ln \left (t \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.144 |
|
| \(184\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-1+x \right ) y^{\prime \prime \prime \prime }+\left (x +5\right ) y^{\prime \prime }+\tan \left (x \right ) y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.141 |
|
| \(185\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.192 |
|
| \(186\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )}&=0 \end {array} \]
|
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.488 |
|
| \(187\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.110 |
|
| \(188\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y x +\left (x^{2}+2\right ) y^{\prime }-2 y^{\prime \prime } x +\left (x^{2}+2\right ) y^{\prime \prime \prime }&=x^{4}+12 \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.146 |
|
| \(189\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5}&=0 \end {array} \]
|
[[_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.612 |
|
| \(190\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} y^{\prime \prime \prime }-\left (3 y y^{\prime }+2 x y^{2}\right ) y^{\prime \prime }+\left (2 {y^{\prime }}^{2}+2 y y^{\prime } x +3 y^{2} x^{2}\right ) y^{\prime }+x^{3} y^{3}&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.119 |
|
| \(191\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 16 \left (x +1\right )^{4} y^{\prime \prime \prime \prime }+96 \left (x +1\right )^{3} y^{\prime \prime \prime }+104 \left (x +1\right )^{2} y^{\prime \prime }+8 \left (x +1\right ) y^{\prime }+y&=x^{2}+4 x +3 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.164 |
|
| \(192\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{3}+x +1\right ) y^{\prime \prime \prime }+\left (3+6 x \right ) y^{\prime \prime }+6 y&=0 \end {array} \]
|
[[_3rd_order, _exact, _linear, _homogeneous]] |
✗ |
✗ |
✗ |
9.803 |
|
| \(193\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.112 |
|
| \(194\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y x +\left (x^{2}+2\right ) y^{\prime }+4 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=2 \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.113 |
|
| \(195\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+y^{\prime } x +y&=\ln \left (x \right ) \end {array} \]
|
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
1.700 |
|
| \(196\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+\left (2 y x -1\right ) y^{\prime }+y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.122 |
|
| \(197\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime } x -y^{\prime }+y x&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.161 |
|
| \(198\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x -1\right )^{3} y^{\prime \prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.142 |
|
| \(199\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 16 \left (x +1\right )^{4} y^{\prime \prime \prime \prime }+96 \left (x +1\right )^{3} y^{\prime \prime \prime }+104 \left (x +1\right )^{2} y^{\prime \prime }+8 \left (x +1\right ) y^{\prime }+y&=x^{2}+4 x +3 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.191 |
|
| \(200\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime \prime }-x^{\prime }&=0\\ x \left (0\right )&=1\\ x \left (\infty \right )&=0\\ \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
2.962 |
|
| \(201\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime \prime }-3 x^{\prime }+k x&=0\\ x \left (0\right )&=1\\ x \left (\infty \right )&=0\\ \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✗ |
✗ |
362.994 |
|
| \(202\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime \prime \prime }-4 x^{\prime \prime }+x&=0\\ x \left (0\right )&=0\\ x \left (\infty \right )&=0\\ x^{\prime }\left (0\right )&=1\\ \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
12.342 |
|
| \(203\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 {b^{\prime \prime \prime \prime }}^{5}+7 {b^{\prime }}^{10}+b^{7}-b^{5}&=p \end {array} \]
|
[NONE] |
✗ |
✗ |
✗ |
0.158 |
|
| \(204\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+x y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-y^{\prime } x +\sin \left (y\right )&=0 \end {array} \]
|
[NONE] |
✗ |
✗ |
✗ |
0.168 |
|
| \(205\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime \prime \prime }+y^{\prime } x +y&=x^{2} \end {array} \]
|
[[_3rd_order, _exact, _nonlinear]] |
✗ |
✗ |
✗ |
0.131 |
|
| \(206\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+x^{2} y^{\prime \prime \prime }+y^{\prime \prime } x -{\mathrm e}^{x} y^{\prime }+2 y&=x^{2}+x +1 \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.208 |
|
| \(207\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime }+y&=5 \sin \left (x \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.146 |
|
| \(208\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {s^{\prime \prime \prime }}^{2}+{s^{\prime \prime }}^{3}&=s-3 t \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.138 |
|
| \(209\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }&=\frac {24 x +24 y}{x^{3}} \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
0.151 |
|
| \(210\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime \prime }+2 y^{\prime \prime } x -y^{\prime } x -2 y x&=1 \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
0.141 |
|
| \(211\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+x^{2} y&={\mathrm e}^{x} \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.131 |
|
| \(212\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y y^{\prime \prime \prime \prime }&=5 \end {array} \]
|
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.151 |
|
| \(213\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }+y x&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.132 |
|
| \(214\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime \prime }+4 y^{\prime \prime } x -y x&=1 \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
0.124 |
|
| \(215\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{3}-1\right ) y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y x&=0\\ y \left (-1\right )&=0\\ y^{\prime }\left (-1\right )&=2\\ y^{\prime \prime }\left (-1\right )&=2\\ \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.166 |
|
| \(216\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x y^{\prime \prime \prime }-4 y x&=\cos \left (y\right ) \end {array} \]
|
[NONE] |
✗ |
✗ |
✗ |
0.138 |
|
| \(217\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-3 y^{\prime \prime } x +4 y&=x^{2} \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
0.129 |
|
| \(218\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (5\right )}-y^{\prime }-\frac {4 y}{x}&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
0.185 |
|
| \(219\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+y^{4}&=0 \end {array} \]
|
[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.157 |
|
| \(220\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (5\right )}+t y^{\prime \prime }-3 y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
0.186 |
|
| \(221\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y&=0 \end {array} \]
|
[NONE] |
✗ |
✗ |
✗ |
0.135 |
|
| \(222\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
0.173 |
|
| \(223\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (t \right ) y^{\prime \prime \prime }-\cos \left (t \right ) y^{\prime }&=2 \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✗ |
3.082 |
|
| \(224\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime }}^{2}-y^{\prime \prime \prime } y^{\prime }&=\frac {{y^{\prime }}^{2}}{x^{2}} \end {array} \]
|
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.886 |
|
| \(225\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} y^{\prime \prime \prime }-3 y y^{\prime } y^{\prime \prime }+2 {y^{\prime }}^{3}+\frac {y \left (y y^{\prime \prime }-{y^{\prime }}^{2}\right )}{x}&=\frac {y^{3}}{x^{2}} \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.168 |
|
| \(226\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime \prime }+4 x y^{\prime \prime \prime }+2 y^{\prime \prime }&=0\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=0\\ y \left (0\right )&=y_{0}\\ \end {array} \]
|
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
7.773 |
|
| \(227\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 y^{\prime \prime } x&=0\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=0\\ y \left (0\right )&=y_{0}\\ \end {array} \]
|
[[_high_order, _missing_y]] |
✗ |
✗ |
✗ |
11.843 |
|
| \(228\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime \prime \prime }&=y^{\prime } y^{\prime \prime } \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✗ |
0.039 |
|
| \(229\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime \prime }}^{2}-y^{\prime \prime \prime } y^{\prime }&=\frac {{y^{\prime }}^{2}}{x^{2}} \end {array} \]
|
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.268 |
|
| \(230\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} \left (y^{\prime \prime \prime } y^{\prime }-2 {y^{\prime \prime }}^{2}\right )&={y^{\prime }}^{4} \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.049 |
|
| \(231\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y y^{\prime \prime \prime }&=y^{\prime } \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✗ |
0.033 |
|
| \(232\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} y^{\prime \prime \prime }&={y^{\prime }}^{3} \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.035 |
|
| \(233\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} \left (x^{3} y^{\prime \prime \prime }-2 y^{\prime } x -3 y\right )&=x^{3} y^{\prime } \left (3 y y^{\prime \prime }-2 {y^{\prime }}^{2}\right ) \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.053 |
|
| \(234\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime \prime }}^{2}\right ) y&={y^{\prime }}^{5} \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.045 |
|
| \(235\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} \left (y^{\prime \prime \prime } y^{\prime }-2 y^{\prime \prime }\right )&=y {y^{\prime }}^{2} y^{\prime \prime }+2 {y^{\prime }}^{4} \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
0.058 |
|
| \(236\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (y^{2} y^{\prime \prime \prime }-{y^{\prime }}^{3}\right )&=2 y^{2} y^{\prime }-3 x y {y^{\prime }}^{2} \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✗ |
✗ |
0.050 |
|
| \(237\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime \prime }-3 {y^{\prime }}^{2}&=0\\ y \left (0\right )&=-3\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=-1\\ \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✗ |
✗ |
5.281 |
|
| \(238\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }&=3 y y^{\prime }\\ y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&={\frac {9}{2}}\\ \end {array} \]
|
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
✗ |
✗ |
0.056 |
|
| \(239\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x +3\right )^{3} y^{\prime \prime \prime }+3 \left (2 x +3\right ) y^{\prime }-6 y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.042 |
|
| \(240\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.036 |
|
| \(241\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-2 x +3\right ) y^{\prime \prime \prime }-\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.049 |
|
| \(242\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=f \left (x \right )\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=0\\ y^{\prime \prime }\left (1\right )&=0\\ \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.072 |
|
| \(243\) |
\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z w^{\prime \prime \prime }+w&=0 \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
0.033 |
|