2.7.1 higher order Euler ode

Table 2.1189: higher order Euler ode [202]

#

ODE

CAS classification

Solved

Maple

Mma

Sympy

time(sec)

255

\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\ y \left (1\right ) &= 6 \\ y^{\prime }\left (1\right ) &= 14 \\ y^{\prime \prime }\left (1\right ) &= 22 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.145

256

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 5 \\ y^{\prime \prime }\left (1\right ) &= -11 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.132

314

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

[[_3rd_order, _with_linear_symmetries]]

0.526

317

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x&=0 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.098

318

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

[[_3rd_order, _missing_y]]

0.101

319

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

[[_3rd_order, _missing_y]]

0.095

320

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

[[_3rd_order, _missing_y]]

0.101

321

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y&=0 \\ \end{align*}

[[_3rd_order, _exact, _linear, _homogeneous]]

0.099

958

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x&=0 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.116

959

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

[[_3rd_order, _missing_y]]

0.120

960

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

[[_3rd_order, _missing_y]]

0.114

961

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

[[_3rd_order, _missing_y]]

0.122

962

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y&=0 \\ \end{align*}

[[_3rd_order, _exact, _linear, _homogeneous]]

0.120

1467

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.152

2106

\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (-1\right ) &= -4 \\ y^{\prime }\left (-1\right ) &= -14 \\ y^{\prime \prime }\left (-1\right ) &= -20 \\ \end{align*}

[[_3rd_order, _exact, _linear, _homogeneous]]

0.236

2108

\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}

[[_3rd_order, _exact, _linear, _homogeneous]]

0.213

2109

\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}

[[_3rd_order, _exact, _linear, _homogeneous]]

0.200

2110

\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 1 \\ \end{align*}

[[_3rd_order, _exact, _linear, _homogeneous]]

0.204

2111

\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= k_{0} \\ y^{\prime }\left (1\right ) &= k_{1} \\ y^{\prime \prime }\left (1\right ) &= k_{2} \\ \end{align*}

[[_3rd_order, _exact, _linear, _homogeneous]]

0.197

2221

\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=2 x \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.306

2222

\begin{align*} 4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 y^{\prime } x +2 y&=30 x^{2} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.339

2223

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

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.302

2224

\begin{align*} 16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 y^{\prime } x +9 y&=96 x^{{5}/{2}} \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.425

2225

\begin{align*} x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 y^{\prime } x +24 y&=x^{4} \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.393

2226

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=12 x^{2} \\ \end{align*}

[[_high_order, _exact, _linear, _nonhomogeneous]]

0.398

2227

\begin{align*} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=4 x \\ y \left (1\right ) &= 4 \\ y^{\prime }\left (1\right ) &= 4 \\ y^{\prime \prime }\left (1\right ) &= 2 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.363

2228

\begin{align*} x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y&=x^{3} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 7 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.375

2229

\begin{align*} x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+16 y^{\prime } x -16 y&=9 x^{4} \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 5 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.388

2230

\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \left (x +1\right ) \\ y \left (-1\right ) &= -6 \\ y^{\prime }\left (-1\right ) &= {\frac {43}{6}} \\ y^{\prime \prime }\left (-1\right ) &= -{\frac {5}{2}} \\ \end{align*}

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.351

2231

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=9 x^{2} \\ y \left (1\right ) &= -7 \\ y^{\prime }\left (1\right ) &= -11 \\ y^{\prime \prime }\left (1\right ) &= -5 \\ y^{\prime \prime \prime }\left (1\right ) &= 6 \\ \end{align*}

[[_high_order, _exact, _linear, _nonhomogeneous]]

0.462

2232

\begin{align*} 4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-y^{\prime } x +y&=6 x \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 4 \\ y^{\prime \prime \prime }\left (1\right ) &= -{\frac {37}{4}} \\ \end{align*}

[[_high_order, _exact, _linear, _nonhomogeneous]]

0.447

2233

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 y^{\prime } x +6 y&=40 x^{3} \\ y \left (-1\right ) &= -1 \\ y^{\prime }\left (-1\right ) &= -7 \\ y^{\prime \prime }\left (-1\right ) &= -1 \\ y^{\prime \prime \prime }\left (-1\right ) &= -31 \\ \end{align*}

[[_high_order, _exact, _linear, _nonhomogeneous]]

0.453

2235

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

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.335

2237

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=F \left (x \right ) \\ \end{align*}

[[_high_order, _exact, _linear, _nonhomogeneous]]

0.430

3228

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=\frac {1}{x} \\ \end{align*}

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.282

3232

\begin{align*} 4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right )+x \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.312

3233

\begin{align*} 3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 y^{\prime } x +10 y&=\frac {4}{x^{2}} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.424

3234

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 y^{\prime } x -6 y&=\cos \left (\ln \left (x \right )\right ) \\ \end{align*}

[[_high_order, _exact, _linear, _nonhomogeneous]]

1.355

3235

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

[[_3rd_order, _linear, _nonhomogeneous]]

0.688

3708

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.148

3709

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

[[_3rd_order, _missing_y]]

0.144

4164

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.172

4510

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=9 \ln \left (x \right ) x^{2} \\ \end{align*}

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.417

4512

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

[[_3rd_order, _with_linear_symmetries]]

1.076

6692

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

[[_3rd_order, _quadrature]]

0.301

6693

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

[[_3rd_order, _with_linear_symmetries]]

0.164

6694

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

[[_3rd_order, _with_linear_symmetries]]

0.352

6695

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

[[_3rd_order, _with_linear_symmetries]]

0.175

6696

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

[[_3rd_order, _with_linear_symmetries]]

0.380

6697

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

[[_3rd_order, _with_linear_symmetries]]

0.182

6698

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

[[_3rd_order, _missing_y]]

0.180

6699

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.167

6700

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.178

6701

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

[[_3rd_order, _missing_y]]

0.313

6702

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

[[_3rd_order, _with_linear_symmetries]]

0.177

6703

\begin{align*} -8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.177

6705

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

[[_3rd_order, _with_linear_symmetries]]

0.173

6707

\begin{align*} -\left (-a \,x^{3}+12\right ) y+6 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.380

6715

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

[[_3rd_order, _with_linear_symmetries]]

0.160

6717

\begin{align*} 2 y x +2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=10 x^{2}+10 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.644

6718

\begin{align*} y x -x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=1 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.302

6775

\begin{align*} -4 y-2 y^{\prime } x +4 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.202

6776

\begin{align*} y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.196

6777

\begin{align*} 12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _missing_y]]

0.179

6778

\begin{align*} a y+12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.208

6779

\begin{align*} \operatorname {A4} y+\operatorname {A3} x y^{\prime }+\operatorname {A2} \,x^{2} y^{\prime \prime }+\operatorname {A1} \,x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.431

7972

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

[[_3rd_order, _with_linear_symmetries]]

0.260

8027

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

[[_3rd_order, _missing_y]]

0.332

8028

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

[[_3rd_order, _with_linear_symmetries]]

0.246

8174

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=12 x^{2} \\ \end{align*}

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.262

8207

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 y^{\prime } x -78 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.119

8763

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

[[_high_order, _with_linear_symmetries]]

0.292

8958

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

[[_3rd_order, _with_linear_symmetries]]

0.162

8978

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.169

9310

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

[[_3rd_order, _missing_y]]

0.164

9311

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.180

9312

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

[[_3rd_order, _with_linear_symmetries]]

0.179

9889

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

[[_3rd_order, _with_linear_symmetries]]

0.192

10150

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

[[_3rd_order, _with_linear_symmetries]]

0.264

10151

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

[[_3rd_order, _with_linear_symmetries]]

3.849

10152

\begin{align*} 5 x^{5} y^{\prime \prime \prime \prime }+4 x^{4} y^{\prime \prime \prime }+x^{2} y^{\prime }+y x&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.404

12742

\begin{align*} x^{2} y^{\prime \prime \prime }+3 y^{\prime \prime } x +\left (4 a^{2} x^{2 a}+1-4 \nu ^{2} a^{2}\right ) y^{\prime }&=4 a^{3} x^{2 a -1} y \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.463

12760

\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y-6 x^{3} \left (x -1\right ) \ln \left (x \right )+x^{3} \left (8+x \right )&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.280

12763

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+\left (a \,x^{3}-12\right ) y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.205

12766

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

[[_3rd_order, _linear, _nonhomogeneous]]

13.319

12811

\begin{align*} 12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _missing_y]]

0.105

12812

\begin{align*} a y+12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.134

14116

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

[[_3rd_order, _with_linear_symmetries]]

0.693

14117

\begin{align*} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=10 x +\frac {10}{x} \\ \end{align*}

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

1.444

14125

\begin{align*} y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=\left (1+\ln \left (x \right )\right )^{2} \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

1.738

14131

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=\frac {1}{x} \\ \end{align*}

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.656

14424

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 y^{\prime } x -8 y&=0 \\ \end{align*}

[[_3rd_order, _fully, _exact, _linear]]

0.437

14435

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

[[_3rd_order, _with_linear_symmetries]]

0.633

14565

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

[[_3rd_order, _with_linear_symmetries]]

0.479

14708

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

[[_3rd_order, _with_linear_symmetries]]

0.460

14709

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 y^{\prime } x -8 y&=0 \\ \end{align*}

[[_3rd_order, _fully, _exact, _linear]]

0.476

14710

\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-6 y^{\prime } x +18 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.484

14716

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

[[_3rd_order, _with_linear_symmetries]]

0.671

14830

\begin{align*} t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 t x^{\prime }-6 x&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.446

15517

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

[[_3rd_order, _with_linear_symmetries]]

0.114

16576

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

[[_3rd_order, _with_linear_symmetries]]

0.177

16577

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

[[_3rd_order, _with_linear_symmetries]]

0.175

16578

\begin{align*} x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.180

16579

\begin{align*} -8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.176

16580

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 y^{\prime } x +16 y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.214

16581

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y&=0 \\ \end{align*}

[[_high_order, _exact, _linear, _homogeneous]]

0.205

16582

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

[[_high_order, _with_linear_symmetries]]

0.204

16583

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}

[[_high_order, _exact, _linear, _homogeneous]]

0.205

16703

\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=x^{3} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.320

16704

\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&={\mathrm e}^{-x^{2}} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.465

16707

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y&=12 x \sin \left (x^{2}\right ) \\ \end{align*}

[[_high_order, _exact, _linear, _nonhomogeneous]]

0.515

17611

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

[[_3rd_order, _with_linear_symmetries]]

0.540

17625

\begin{align*} x^{3} y^{\prime \prime \prime }+22 x^{2} y^{\prime \prime }+124 y^{\prime } x +140 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.326

17626

\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }-46 y^{\prime } x +100 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.246

17627

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

[[_3rd_order, _with_linear_symmetries]]

0.254

17628

\begin{align*} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\ \end{align*}

[[_3rd_order, _exact, _linear, _homogeneous]]

0.360

17629

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

[[_3rd_order, _with_linear_symmetries]]

0.307

17630

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.294

17631

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y&=0 \\ \end{align*}

[[_3rd_order, _exact, _linear, _homogeneous]]

0.271

17641

\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-11 y^{\prime } x +16 y&=\frac {1}{x^{3}} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.549

17642

\begin{align*} x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+70 y^{\prime } x +80 y&=\frac {1}{x^{13}} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.621

17647

\begin{align*} x^{3} y^{\prime \prime \prime }+10 x^{2} y^{\prime \prime }-20 y^{\prime } x +20 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= -1 \\ y^{\prime \prime }\left (1\right ) &= 1 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.363

17648

\begin{align*} x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 y^{\prime } x +42 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.408

17649

\begin{align*} x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+5 y^{\prime } x -5 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= -1 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.467

17650

\begin{align*} x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+17 y^{\prime } x -17 y&=0 \\ y \left (1\right ) &= -2 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.365

17658

\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 y^{\prime } x&=0 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.266

17659

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

[[_3rd_order, _missing_y]]

0.379

17660

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

[[_3rd_order, _with_linear_symmetries]]

0.303

17661

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

[[_3rd_order, _missing_y]]

0.480

17673

\begin{align*} x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 y^{\prime } x +125 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.266

17674

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 y^{\prime } x +48 y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.306

17675

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+14 x^{3} y^{\prime \prime \prime }+55 x^{2} y^{\prime \prime }+65 y^{\prime } x +15 y&=0 \\ \end{align*}

[[_high_order, _exact, _linear, _homogeneous]]

0.380

17676

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+35 y^{\prime } x +45 y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.469

17677

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 y^{\prime } x +4 y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.327

17678

\begin{align*} x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 y^{\prime } x +58 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 10 \\ y^{\prime \prime }\left (1\right ) &= -2 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.402

18985

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.163

19164

\begin{align*} 2 x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+12 y^{\prime } x -12 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.183

19165

\begin{align*} y^{\prime \prime \prime }-\frac {3 y^{\prime \prime }}{x}+\frac {6 y^{\prime }}{x^{2}}-\frac {6 y}{x^{3}}&=0 \\ \end{align*}

[[_3rd_order, _fully, _exact, _linear]]

0.177

19169

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

[[_3rd_order, _with_linear_symmetries]]

0.179

19201

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

[[_3rd_order, _with_linear_symmetries]]

0.381

19547

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

[[_3rd_order, _missing_y]]

0.157

19548

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.172

19549

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

[[_3rd_order, _with_linear_symmetries]]

0.168

19760

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 y^{\prime } x&=17 x^{6} \\ \end{align*}

[[_high_order, _missing_y]]

0.443

19761

\begin{align*} t^{4} x^{\prime \prime \prime \prime }-2 t^{3} x^{\prime \prime \prime }-20 t^{2} x^{\prime \prime }+12 t x^{\prime }+16 x&=\cos \left (3 \ln \left (t \right )\right ) \\ \end{align*}

[[_high_order, _exact, _linear, _nonhomogeneous]]

1.200

19768

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

[[_3rd_order, _with_linear_symmetries]]

0.216

19787

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

[[_3rd_order, _with_linear_symmetries]]

0.211

19853

\begin{align*} x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 y^{\prime } x&=\ln \left (x \right )^{2} \\ \end{align*}

[[_3rd_order, _missing_y]]

0.353

19855

\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=x^{3} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.326

19856

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

[[_3rd_order, _with_linear_symmetries]]

0.358

19857

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.184

20094

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.215

20095

\begin{align*} y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.254

20102

\begin{align*} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}}&=1 \\ \end{align*}

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.538

20104

\begin{align*} -8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.210

20106

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.205

20107

\begin{align*} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=10 c +\frac {10}{x} \\ \end{align*}

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.690

20111

\begin{align*} y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=\left (1+\ln \left (x \right )\right )^{2} \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.941

20112

\begin{align*} y x -x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=1 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.348

20486

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.131

20488

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

[[_3rd_order, _with_linear_symmetries]]

0.305

20489

\begin{align*} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}}&=1 \\ \end{align*}

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.434

20491

\begin{align*} -8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.131

20505

\begin{align*} y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=4 x \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.786

20506

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 y^{\prime } x +2 y&=x^{2}+3 x -4 \\ \end{align*}

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.466

20508

\begin{align*} -8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x^{2}+\frac {1}{x^{2}} \\ \end{align*}

[[_3rd_order, _reducible, _mu_y2]]

0.349

20509

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

[[_high_order, _with_linear_symmetries]]

0.450

20512

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

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.306

20513

\begin{align*} y+3 y^{\prime } x +9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=\left (1+\ln \left (x \right )\right )^{2} \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.669

20519

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 y^{\prime } x +2 y&=x^{2}+3 x -4 \\ \end{align*}

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.396

20538

\begin{align*} x^{3} y^{\prime \prime \prime }&=1 \\ \end{align*}

[[_3rd_order, _quadrature]]

0.232

20582

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

[[_3rd_order, _with_linear_symmetries]]

0.140

20610

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.138

20746

\begin{align*} y x -x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime }&=1 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.244

20748

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

[[_3rd_order, _with_linear_symmetries]]

0.274

20749

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.098

20750

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.116

20752

\begin{align*} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=10 x +\frac {10}{x} \\ \end{align*}

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.607

20866

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

[[_3rd_order, _with_linear_symmetries]]

0.091

21203

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.106

21558

\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=4 \ln \left (x \right ) \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.422

22483

\begin{align*} x^{3} y^{\prime \prime \prime }&=1+\sqrt {x} \\ \end{align*}

[[_3rd_order, _quadrature]]

0.354

22762

\begin{align*} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x +1 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.414

22763

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

[[_3rd_order, _with_linear_symmetries]]

0.445

22764

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+y^{\prime } x -y&=1 \\ \end{align*}

[[_high_order, _exact, _linear, _nonhomogeneous]]

0.613

23376

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

[[_3rd_order, _with_linear_symmetries]]

0.357

23381

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

[[_3rd_order, _with_linear_symmetries]]

0.364

23386

\begin{align*} 8 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ y^{\prime \prime }\left (1\right ) &= 0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.494

23387

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

[[_3rd_order, _with_linear_symmetries]]

0.399

23388

\begin{align*} x^{4} y^{\prime \prime \prime \prime }-5 x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 y^{\prime } x +6 y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.483

23389

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

[[_high_order, _with_linear_symmetries]]

0.427

23390

\begin{align*} 2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-12 y^{\prime } x -2 y&=0 \\ \end{align*}

[[_3rd_order, _exact, _linear, _homogeneous]]

0.358

23391

\begin{align*} x^{5} y^{\left (5\right )}-2 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }&=0 \\ \end{align*}

[[_high_order, _missing_y]]

0.442

23392

\begin{align*} 7 x^{4} y^{\prime \prime \prime \prime }-2 x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-6 y^{\prime } x +6 y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.415

23393

\begin{align*} x^{5} y^{\left (5\right )}+3 x^{3} y^{\prime \prime \prime }-9 x^{2} y^{\prime \prime }+18 y^{\prime } x -18 y&=0 \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.447

23394

\begin{align*} x^{6} y^{\left (6\right )}-12 x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _missing_y]]

0.453

23395

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.348

23397

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

[[_3rd_order, _with_linear_symmetries]]

0.344

25670

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=12 x^{2} \\ \end{align*}

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.354

25690

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 y^{\prime } x -78 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.187

26039

\begin{align*} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=x +1 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.205

26042

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

[[_3rd_order, _missing_y]]

0.210