2.1.6 Problems not solved. Higher order only

Table 2.11: Problems not solved. Higher order only. [227]

#

ID

ODE

CAS classification

Maple

Mma

Sympy

time(sec)

\(1\)

1463

\begin{align*} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.070

\(2\)

1469

\begin{align*} t y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }+t y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.037

\(3\)

1470

\begin{align*} \left (2-t \right ) y^{\prime \prime \prime }+\left (2 t -3\right ) y^{\prime \prime }-y^{\prime } t +y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.063

\(4\)

1471

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.072

\(5\)

3497

\begin{align*} 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{align*}

[[_3rd_order, _exact, _nonlinear]]

0.049

\(6\)

6608

\begin{align*} y^{\prime \prime \prime }&=y x \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.028

\(7\)

6620

\begin{align*} y+2 y^{\prime } x +y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.034

\(8\)

6621

\begin{align*} a y+2 a x y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.033

\(9\)

6622

\begin{align*} y f^{\prime }\left (x \right )+2 f \left (x \right ) y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.043

\(10\)

6660

\begin{align*} -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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.043

\(11\)

6661

\begin{align*} a^{3} x^{3} y+3 a^{2} x^{2} y^{\prime }+3 a x y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.042

\(12\)

6662

\begin{align*} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.039

\(13\)

6663

\begin{align*} -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{align*}

[[_3rd_order, _missing_y]]

4.066

\(14\)

6665

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.066

\(15\)

6666

\begin{align*} f \left (x \right ) y+y^{\prime }+f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.038

\(16\)

6671

\begin{align*} y x +3 y^{\prime }+x y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.034

\(17\)

6672

\begin{align*} -y+y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.038

\(18\)

6673

\begin{align*} y-y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.036

\(19\)

6674

\begin{align*} y-y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=-x^{2}+1 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.042

\(20\)

6675

\begin{align*} -x^{2} y+3 y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.040

\(21\)

6678

\begin{align*} a \,x^{2} y-6 y^{\prime }+x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.042

\(22\)

6680

\begin{align*} 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{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.046

\(23\)

6683

\begin{align*} a \,x^{2} y+6 y^{\prime }+6 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.041

\(24\)

6685

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.052

\(25\)

6686

\begin{align*} 10 y^{\prime }+8 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.619

\(26\)

6687

\begin{align*} -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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.041

\(27\)

6688

\begin{align*} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.043

\(28\)

6691

\begin{align*} 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{align*}

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

1.490

\(29\)

6706

\begin{align*} -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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.046

\(30\)

6708

\begin{align*} -y+2 y^{\prime } x +x^{2} \ln \left (x \right ) y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=2 x^{3} \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

1.427

\(31\)

6710

\begin{align*} -12 y+3 \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.042

\(32\)

6713

\begin{align*} -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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.055

\(33\)

6714

\begin{align*} -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{align*}

[NONE]

0.041

\(34\)

6716

\begin{align*} 2 y+\left (1-2 x \right ) y^{\prime }+\left (1-2 x \right )^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.040

\(35\)

6720

\begin{align*} -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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.051

\(36\)

6722

\begin{align*} -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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.050

\(37\)

6723

\begin{align*} \left (a -x \right )^{3} \left (b -x \right )^{3} y^{\prime \prime \prime }&=c y \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.044

\(38\)

6747

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.057

\(39\)

6750

\begin{align*} y^{2}-2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]]

0.034

\(40\)

6751

\begin{align*} y^{2}-2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x^{3} \\ \end{align*}

[NONE]

0.034

\(41\)

6759

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.054

\(42\)

6769

\begin{align*} -a^{2} y+12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.043

\(43\)

6771

\begin{align*} -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{align*}

[[_high_order, _with_linear_symmetries]]

0.049

\(44\)

6772

\begin{align*} -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{align*}

[[_high_order, _with_linear_symmetries]]

0.047

\(45\)

6774

\begin{align*} -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{align*}

[[_high_order, _with_linear_symmetries]]

0.058

\(46\)

6780

\begin{align*} -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{align*}

[[_high_order, _with_linear_symmetries]]

0.063

\(47\)

6791

\begin{align*} -y y^{\prime }+{y^{\prime }}^{2}+y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

0.031

\(48\)

6792

\begin{align*} a y y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

0.029

\(49\)

6793

\begin{align*} 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{align*}

[[_3rd_order, _exact, _nonlinear]]

0.040

\(50\)

6794

\begin{align*} \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{align*}

[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

0.041

\(51\)

6795

\begin{align*} y^{3} y^{\prime }-y^{\prime } y^{\prime \prime }+y y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]

0.040

\(52\)

6796

\begin{align*} 3 y^{\prime } y^{\prime \prime }+\left (a +y\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

0.035

\(53\)

6797

\begin{align*} 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{align*}

[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]

0.049

\(54\)

6798

\begin{align*} 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{align*}

[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]

0.044

\(55\)

6799

\begin{align*} 15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

0.041

\(56\)

6800

\begin{align*} 40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

0.037

\(57\)

6813

\begin{align*} 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{align*}

[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]

0.095

\(58\)

8054

\begin{align*} \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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.043

\(59\)

8058

\begin{align*} \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{align*}

[[_3rd_order, _exact, _nonlinear]]

0.046

\(60\)

8059

\begin{align*} 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{align*}

[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]

0.070

\(61\)

8060

\begin{align*} 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{align*}

[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]

0.051

\(62\)

8152

\begin{align*} x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y&=0 \\ \end{align*}

[NONE]

0.031

\(63\)

8153

\begin{align*} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.041

\(64\)

8760

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime } x +4 x^{2} y^{\prime }+8 x^{3} y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.043

\(65\)

8970

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.045

\(66\)

10132

\begin{align*} y^{\prime \prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3}&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.042

\(67\)

10458

\begin{align*} y^{\prime \prime \prime }-y x&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.039

\(68\)

12709

\begin{align*} y^{\prime \prime \prime }+y a \,x^{3}-b x&=0 \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.037

\(69\)

12710

\begin{align*} y^{\prime \prime \prime }-a \,x^{b} y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.033

\(70\)

12713

\begin{align*} a y+2 a x y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.036

\(71\)

12714

\begin{align*} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+\left (a +b -1\right ) x y^{\prime }-a b y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.042

\(72\)

12715

\begin{align*} y^{\prime \prime \prime }+x^{2 c -2} y^{\prime }+\left (c -1\right ) x^{2 c -3} y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.057

\(73\)

12716

\begin{align*} y^{\prime \prime \prime }-\left (6 k^{2} \sin \left (x \right )^{2}+a \right ) y^{\prime }+b y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.048

\(74\)

12717

\begin{align*} y f^{\prime }\left (x \right )+2 f \left (x \right ) y^{\prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.041

\(75\)

12722

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.042

\(76\)

12723

\begin{align*} a^{3} x^{3} y+3 a^{2} x^{2} y^{\prime }+3 a x y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.041

\(77\)

12725

\begin{align*} f \left (x \right ) y+y^{\prime }+f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.038

\(78\)

12726

\begin{align*} y^{\prime \prime \prime }+f \left (x \right ) \left (x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y\right )&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.043

\(79\)

12728

\begin{align*} x y^{\prime \prime \prime }+3 y^{\prime \prime }+y x&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.033

\(80\)

12729

\begin{align*} x y^{\prime \prime \prime }+3 y^{\prime \prime }-a \,x^{2} y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.037

\(81\)

12730

\begin{align*} x y^{\prime \prime \prime }+\left (a +b \right ) y^{\prime \prime }-y^{\prime } x -a y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.038

\(82\)

12731

\begin{align*} x y^{\prime \prime \prime }-\left (x +2 v \right ) y^{\prime \prime }-\left (x -2 v -1\right ) y^{\prime }+\left (x -1\right ) y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.041

\(83\)

12733

\begin{align*} 2 x y^{\prime \prime \prime }+3 y^{\prime \prime }+a x y-b&=0 \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.036

\(84\)

12734

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.048

\(85\)

12735

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.046

\(86\)

12737

\begin{align*} \left (2 x -1\right ) y^{\prime \prime \prime }-8 y^{\prime } x +8 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.036

\(87\)

12739

\begin{align*} a \,x^{2} y-6 y^{\prime }+x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.036

\(88\)

12740

\begin{align*} x^{2} y^{\prime \prime \prime }+\left (x +1\right ) y^{\prime \prime }-y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.034

\(89\)

12743

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.052

\(90\)

12744

\begin{align*} 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{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.042

\(91\)

12747

\begin{align*} a \,x^{2} y+6 y^{\prime }+6 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.040

\(92\)

12748

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.044

\(93\)

12749

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.044

\(94\)

12750

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.046

\(95\)

12751

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.046

\(96\)

12752

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.045

\(97\)

12753

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.043

\(98\)

12755

\begin{align*} -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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.039

\(99\)

12756

\begin{align*} 2 x \left (x -1\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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.043

\(100\)

12757

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.043

\(101\)

12758

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.041

\(102\)

12759

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.075

\(103\)

12762

\begin{align*} -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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.043

\(104\)

12764

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.065

\(105\)

12765

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.042

\(106\)

12767

\begin{align*} -12 y+3 \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.043

\(107\)

12768

\begin{align*} \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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.043

\(108\)

12769

\begin{align*} 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 {a1} \operatorname {a3} +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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.057

\(109\)

12770

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.045

\(110\)

12772

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.048

\(111\)

12773

\begin{align*} x^{6} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.037

\(112\)

12774

\begin{align*} x^{6} y^{\prime \prime \prime }+6 x^{5} y^{\prime \prime }+a y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.034

\(113\)

12775

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.053

\(114\)

12776

\begin{align*} \left (x -a \right )^{3} \left (-b +x \right )^{3} y^{\prime \prime \prime }-c y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.043

\(115\)

12779

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.065

\(116\)

12780

\begin{align*} y^{\prime \prime \prime }+y^{\prime } x +n y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.036

\(117\)

12781

\begin{align*} y^{\prime \prime \prime }-y^{\prime } x -n y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.033

\(118\)

12788

\begin{align*} y^{\prime \prime \prime \prime }+a \left (b x -1\right ) y^{\prime \prime }+a b y^{\prime }+\lambda y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.042

\(119\)

12789

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.044

\(120\)

12791

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.051

\(121\)

12794

\begin{align*} x y^{\prime \prime \prime \prime }-\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{align*}

[[_high_order, _with_linear_symmetries]]

0.053

\(122\)

12795

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.042

\(123\)

12796

\begin{align*} x^{2} y^{\prime \prime \prime \prime }+2 x y^{\prime \prime \prime }+a y-b \,x^{2}&=0 \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.042

\(124\)

12799

\begin{align*} x^{2} y^{\prime \prime \prime \prime }+6 x y^{\prime \prime \prime }+6 y^{\prime \prime }-\lambda ^{2} y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.043

\(125\)

12801

\begin{align*} x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime }-\lambda ^{2} y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.040

\(126\)

12802

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.048

\(127\)

12803

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.045

\(128\)

12805

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.051

\(129\)

12806

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.091

\(130\)

12807

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.049

\(131\)

12808

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.052

\(132\)

12809

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.057

\(133\)

12810

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.058

\(134\)

12813

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a \right ) x^{3} y^{\prime \prime \prime }+\left (4 x^{2 c} b^{2} c^{2}+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{align*}

[[_high_order, _with_linear_symmetries]]

0.095

\(135\)

12814

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.082

\(136\)

12815

\begin{align*} \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{align*}

[[_high_order, _with_linear_symmetries]]

0.058

\(137\)

12816

\begin{align*} \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{align*}

[[_high_order, _with_linear_symmetries]]

0.063

\(138\)

12818

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.088

\(139\)

12819

\begin{align*} 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{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.070

\(140\)

12822

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.050

\(141\)

12825

\begin{align*} y^{\left (5\right )}-a x y-b&=0 \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.034

\(142\)

12826

\begin{align*} y^{\left (5\right )}+a \,x^{\nu } y^{\prime }+a \nu \,x^{\nu -1} y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.073

\(143\)

12828

\begin{align*} x y^{\left (5\right )}-m n y^{\prime \prime \prime \prime }+a x y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.039

\(144\)

12830

\begin{align*} 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{align*}

[[_high_order, _missing_y]]

0.083

\(145\)

12831

\begin{align*} x^{2} y^{\prime \prime \prime \prime }-a y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.034

\(146\)

12832

\begin{align*} x^{10} y^{\left (5\right )}-a y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.037

\(147\)

12833

\begin{align*} x^{{5}/{2}} y^{\left (5\right )}-a y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.043

\(148\)

12834

\begin{align*} \left (x -a \right )^{5} \left (-b +x \right )^{5} y^{\left (5\right )}-c y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.050

\(149\)

13042

\begin{align*} y^{\prime \prime \prime }+y y^{\prime \prime }-{y^{\prime }}^{2}+1&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

0.033

\(150\)

13043

\begin{align*} y^{\prime \prime \prime }-y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

0.035

\(151\)

13044

\begin{align*} a y y^{\prime \prime }+y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

0.029

\(152\)

13045

\begin{align*} 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{align*}

[[_3rd_order, _exact, _nonlinear]]

0.035

\(153\)

13046

\begin{align*} 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{align*}

[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

0.040

\(154\)

13047

\begin{align*} y^{3} y^{\prime }-y^{\prime } y^{\prime \prime }+y y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]

0.036

\(155\)

13048

\begin{align*} 15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

0.038

\(156\)

13049

\begin{align*} 40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

0.049

\(157\)

13054

\begin{align*} y^{\prime } y^{\prime \prime \prime \prime }-y^{\prime \prime } y^{\prime \prime \prime }+{y^{\prime }}^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]

0.076

\(158\)

13056

\begin{align*} 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{align*}

[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]

0.099

\(159\)

13058

\begin{align*} y^{\prime \prime \prime }&=f \left (y\right ) \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

0.023

\(160\)

14165

\begin{align*} -2 y+2 y^{\prime } x -x^{2} y^{\prime \prime }+\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.042

\(161\)

14166

\begin{align*} y-y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=-x^{2}+1 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.039

\(162\)

14171

\begin{align*} 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{align*}

[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]

0.044

\(163\)

14173

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.041

\(164\)

14832

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.038

\(165\)

15126

\begin{align*} y^{\prime \prime \prime }+y x&=\sin \left (x \right ) \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.035

\(166\)

15129

\begin{align*} y^{\prime \prime }+y y^{\prime \prime \prime \prime }&=1 \\ \end{align*}

[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]]

0.039

\(167\)

15130

\begin{align*} y^{\prime \prime \prime }+y x&=\cosh \left (x \right ) \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.037

\(168\)

15132

\begin{align*} y^{\prime \prime \prime }+y x&=\cosh \left (x \right ) \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.030

\(169\)

15141

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime } x -y^{2}&=\sin \left (x \right ) \\ \end{align*}

[NONE]

0.034

\(170\)

15143

\begin{align*} \sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime }&=1 \\ \end{align*}

[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]]

0.031

\(171\)

15146

\begin{align*} {y^{\prime \prime \prime }}^{2}+\sqrt {y}&=\sin \left (x \right ) \\ \end{align*}

[NONE]

0.058

\(172\)

16444

\begin{align*} y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }&=y \\ \end{align*}

[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

0.032

\(173\)

16468

\begin{align*} x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.036

\(174\)

18124

\begin{align*} 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{align*}

[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

0.065

\(175\)

18967

\begin{align*} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+8 y&=\cos \left (t \right ) \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.065

\(176\)

18968

\begin{align*} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+4 t^{2} y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.060

\(177\)

18969

\begin{align*} y^{\prime \prime \prime }+t y^{\prime \prime }+t^{2} y^{\prime }+t^{2} y&=\ln \left (t \right ) \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.060

\(178\)

18970

\begin{align*} \left (x -4\right ) y^{\prime \prime \prime \prime }+\left (x +1\right ) y^{\prime \prime }+\tan \left (x \right ) y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.081

\(179\)

18971

\begin{align*} \left (x^{2}-2\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+3 y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.061

\(180\)

18973

\begin{align*} t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y&=\cos \left (t \right ) \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.059

\(181\)

18974

\begin{align*} t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.062

\(182\)

18975

\begin{align*} y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 y t^{3}&=\ln \left (t \right ) \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.061

\(183\)

18976

\begin{align*} \left (x -1\right ) y^{\prime \prime \prime \prime }+\left (x +5\right ) y^{\prime \prime }+\tan \left (x \right ) y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.055

\(184\)

18977

\begin{align*} \left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.066

\(185\)

19161

\begin{align*} 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{align*}

[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]

0.176

\(186\)

19170

\begin{align*} -y+y^{\prime } x -y^{\prime \prime }+x y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.048

\(187\)

19174

\begin{align*} -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{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.057

\(188\)

19782

\begin{align*} 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{align*}

[[_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries]]

0.396

\(189\)

19784

\begin{align*} 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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.060

\(190\)

20108

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.075

\(191\)

20153

\begin{align*} \left (x^{3}+x +1\right ) y^{\prime \prime \prime }+\left (3+6 x \right ) y^{\prime \prime }+6 y&=0 \\ \end{align*}

[[_3rd_order, _exact, _linear, _homogeneous]]

22.926

\(192\)

20196

\begin{align*} x^{2} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.059

\(193\)

20529

\begin{align*} 3 y x +\left (x^{2}+2\right ) y^{\prime }+4 y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=2 \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.052

\(194\)

20530

\begin{align*} x^{5} y^{\left (6\right )}+x^{4} y^{\left (5\right )}+y^{\prime } x +y&=\ln \left (x \right ) \\ \end{align*}

[[_high_order, _exact, _linear, _nonhomogeneous]]

0.784

\(195\)

20534

\begin{align*} y^{2}+\left (2 y x -1\right ) y^{\prime }+y^{\prime \prime } x +x^{2} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]

0.054

\(196\)

20609

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime } x -y^{\prime }+y x&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.053

\(197\)

20754

\begin{align*} \left (2 x -1\right )^{3} y^{\prime \prime \prime }+\left (2 x -1\right ) y^{\prime }-2 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.056

\(198\)

20756

\begin{align*} 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{align*}

[[_high_order, _with_linear_symmetries]]

0.076

\(199\)

21181

\begin{align*} x^{\prime \prime \prime }-x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x \left (\infty \right ) &= 0 \\ \end{align*}

[[_3rd_order, _missing_x]]

1.766

\(200\)

21184

\begin{align*} x^{\prime \prime \prime }+a x^{\prime \prime }+b x^{\prime }+c x&=0 \\ x \left (\infty \right ) &= 0 \\ \end{align*}

[[_3rd_order, _missing_x]]

10.998

\(201\)

21185

\begin{align*} x^{\prime \prime \prime }-3 x^{\prime }+k x&=0 \\ x \left (0\right ) &= 1 \\ x \left (\infty \right ) &= 0 \\ \end{align*}

[[_3rd_order, _missing_x]]

8.073

\(202\)

21189

\begin{align*} 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{align*}

[[_high_order, _missing_x]]

0.886

\(203\)

21190

\begin{align*} x^{\prime \prime \prime \prime }-8 x^{\prime \prime \prime }+23 x^{\prime \prime }-28 x^{\prime }+12 x&=0 \\ x \left (\infty \right ) &= 0 \\ \end{align*}

[[_high_order, _missing_x]]

0.443

\(204\)

21194

\begin{align*} x^{\left (5\right )}+x&=0 \\ x \left (\infty \right ) &= 0 \\ \end{align*}

[[_high_order, _missing_x]]

8.886

\(205\)

21952

\begin{align*} 5 {b^{\prime \prime \prime \prime }}^{5}+7 {b^{\prime }}^{10}+b^{7}-b^{5}&=p \\ \end{align*}

0.309

\(206\)

21957

\begin{align*} y^{\prime \prime \prime \prime }+x y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-y^{\prime } x +\sin \left (y\right )&=0 \\ \end{align*}

[NONE]

0.065

\(207\)

22078

\begin{align*} y y^{\prime \prime \prime }+y^{\prime } x +y&=x^{2} \\ \end{align*}

[[_3rd_order, _exact, _nonlinear]]

0.048

\(208\)

22085

\begin{align*} 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{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.081

\(209\)

22089

\begin{align*} y^{\prime \prime \prime }+\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime }+y&=5 \sin \left (x \right ) \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.080

\(210\)

22292

\begin{align*} {s^{\prime \prime \prime }}^{2}+{s^{\prime \prime }}^{3}&=s-3 t \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.566

\(211\)

22799

\begin{align*} y^{\prime \prime \prime }&=\frac {24 x +24 y}{x^{3}} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.054

\(212\)

22800

\begin{align*} x y^{\prime \prime \prime }+2 y^{\prime \prime } x -y^{\prime } x -2 y x&=1 \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.056

\(213\)

23240

\begin{align*} y^{\prime \prime \prime }+x^{2} y&={\mathrm e}^{x} \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.053

\(214\)

23241

\begin{align*} y^{\prime \prime }+y y^{\prime \prime \prime \prime }&=5 \\ \end{align*}

[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]]

0.043

\(215\)

23246

\begin{align*} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }+y x&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.051

\(216\)

23255

\begin{align*} x y^{\prime \prime \prime }+4 y^{\prime \prime } x -y x&=1 \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.051

\(217\)

23291

\begin{align*} \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{align*}

[[_3rd_order, _with_linear_symmetries]]

0.653

\(218\)

23469

\begin{align*} 3 x y^{\prime \prime \prime }-4 y x&=\cos \left (y\right ) \\ \end{align*}

[NONE]

0.044

\(219\)

23472

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime } x +4 y&=x^{2} \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.059

\(220\)

23552

\begin{align*} y^{\left (5\right )}-y^{\prime }-\frac {4 y}{x}&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.060

\(221\)

24464

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\ y \left (0\right ) &= 1 \\ y \left (2\right ) &= 0 \\ y \left (\infty \right ) &= 0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.674

\(222\)

24467

\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+3 y^{\prime }-9 y&=0 \\ y \left (0\right ) &= -1 \\ y \left (1\right ) &= 0 \\ y \left (\infty \right ) &= 0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.567

\(223\)

25144

\begin{align*} y^{\prime \prime \prime \prime }+y^{4}&=0 \\ \end{align*}

[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]]

0.044

\(224\)

25145

\begin{align*} y^{\left (5\right )}+t y^{\prime \prime }-3 y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.071

\(225\)

25649

\begin{align*} x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y&=0 \\ \end{align*}

[NONE]

0.048

\(226\)

25650

\begin{align*} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.067

\(227\)

25654

\begin{align*} \sin \left (t \right ) y^{\prime \prime \prime }-\cos \left (t \right ) y^{\prime }&=2 \\ \end{align*}

[[_3rd_order, _missing_y]]

3.788