2.7.3 higher order ode exact

Table 2.1171: higher order ode exact [93]

#

ODE

CAS classification

Solved

Maple

Mma

Sympy

time(sec)

1466

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

[[_3rd_order, _missing_y]]

0.185

3498

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

[[_3rd_order, _missing_y]]

0.321

6664

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

[[_3rd_order, _fully, _exact, _linear]]

0.247

6670

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

[[_3rd_order, _quadrature]]

0.138

6676

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

[[_3rd_order, _fully, _exact, _linear]]

0.283

6677

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

[[_3rd_order, _missing_y]]

0.238

6679

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

[[_3rd_order, _missing_y]]

0.055

6681

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

[[_3rd_order, _missing_y]]

0.194

6682

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

[[_3rd_order, _missing_y]]

0.167

6684

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

[[_3rd_order, _missing_y]]

0.220

6689

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

[[_3rd_order, _missing_y]]

0.302

6690

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

[[_3rd_order, _missing_y]]

0.181

6709

\begin{align*} 6 y+18 y^{\prime } x +9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _fully, _exact, _linear]]

0.160

6711

\begin{align*} -4 y-14 y^{\prime } x +\left (-8 x^{2}+3\right ) y^{\prime \prime }+x \left (-x^{2}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _fully, _exact, _linear]]

0.212

6724

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

[[_3rd_order, _fully, _exact, _linear]]

0.267

6762

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

[[_high_order, _missing_y]]

0.148

6763

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

[[_high_order, _missing_y]]

0.172

6764

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

[[_high_order, _missing_y]]

0.780

6765

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

[[_high_order, _missing_y]]

0.200

6766

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

[[_high_order, _missing_y]]

0.069

6767

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

[[_high_order, _missing_y]]

0.185

6768

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

[[_high_order, _missing_y]]

0.191

6770

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

[[_high_order, _quadrature]]

0.260

6773

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

[[_high_order, _missing_y]]

0.228

6781

\begin{align*} {\mathrm e}^{x} y+4 \,{\mathrm e}^{x} y^{\prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+\left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _fully, _exact, _linear]]

0.228

8188

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

[[_3rd_order, _missing_y]]

0.187

9313

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

[[_high_order, _missing_y]]

0.302

9846

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

[[_3rd_order, _exact, _linear, _homogeneous]]

1.062

12724

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

[[_3rd_order, _fully, _exact, _linear]]

0.241

12732

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

[[_3rd_order, _fully, _exact, _linear]]

0.222

12736

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.452

12738

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

[[_3rd_order, _missing_y]]

0.260

12745

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

[[_3rd_order, _missing_y]]

0.213

12746

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

[[_3rd_order, _missing_y]]

0.181

12754

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime \prime }+8 y^{\prime \prime } x +10 y^{\prime }-3+\frac {1}{x^{2}}-2 \ln \left (x \right )&=0 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.201

12777

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

[[_3rd_order, _missing_y]]

0.453

12778

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

[[_3rd_order, _fully, _exact, _linear]]

0.263

12793

\begin{align*} x y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-24&=0 \\ \end{align*}

[[_high_order, _missing_y]]

0.161

12797

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

[[_high_order, _missing_y]]

0.075

12798

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

[[_high_order, _missing_y]]

0.197

12800

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

[[_high_order, _missing_y]]

0.210

12804

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

[[_high_order, _missing_y]]

0.254

12817

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

[[_high_order, _fully, _exact, _linear]]

0.261

14167

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

[[_3rd_order, _missing_y]]

0.385

14170

\begin{align*} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 y^{\prime } x +4 y&=0 \\ \end{align*}

[[_3rd_order, _fully, _exact, _linear]]

0.199

14182

\begin{align*} 6 y+18 y^{\prime } x +9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _fully, _exact, _linear]]

0.166

14189

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

[[_3rd_order, _missing_y]]

0.194

15400

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

[[_3rd_order, _quadrature]]

0.167

16398

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

[[_3rd_order, _missing_y]]

0.164

16421

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

[[_3rd_order, _missing_y]]

0.194

17612

\begin{align*} t y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }&=\frac {45}{8 t^{{7}/{2}}} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 1 \\ y^{\prime \prime \prime }\left (1\right ) &= 0 \\ \end{align*}

[[_high_order, _missing_y]]

0.187

17632

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

[[_high_order, _missing_y]]

0.362

18080

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

[[_3rd_order, _quadrature]]

0.163

18101

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

[[_3rd_order, _missing_y]]

0.143

18296

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

[[_3rd_order, _missing_y]]

0.201

18297

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

[[_3rd_order, _missing_y]]

0.203

18298

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

[[_3rd_order, _missing_y]]

0.240

18299

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

[[_3rd_order, _missing_y]]

0.379

18369

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

[[_high_order, _missing_y]]

0.099

18370

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

[[_high_order, _missing_y]]

0.307

18984

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

[[_3rd_order, _missing_y]]

0.131

19171

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

[[_3rd_order, _missing_y]]

0.477

19550

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

[[_high_order, _missing_y]]

0.524

19865

\begin{align*} \left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y&=x^{3} \\ \end{align*}

[[_3rd_order, _fully, _exact, _linear]]

0.557

19866

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

[[_3rd_order, _missing_y]]

0.305

20116

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

[[_3rd_order, _fully, _exact, _linear]]

0.261

20124

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

[[_high_order, _quadrature]]

0.209

20130

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

[[_3rd_order, _missing_y]]

0.184

20140

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

[[_high_order, _missing_y]]

0.417

20154

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

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.311

20157

\begin{align*} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 y^{\prime } x +4 y&=\frac {2}{x^{3}} \\ \end{align*}

[[_3rd_order, _fully, _exact, _linear]]

0.257

20161

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

[[_3rd_order, _missing_y]]

0.235

20166

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

[[_3rd_order, _fully, _exact, _linear]]

0.357

20487

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

[[_3rd_order, _missing_y]]

0.177

20490

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

[[_3rd_order, _missing_y]]

0.180

20493

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

[[_3rd_order, _missing_y]]

0.248

20504

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

[[_3rd_order, _missing_y]]

0.375

20520

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

[[_3rd_order, _fully, _exact, _linear]]

0.307

20531

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

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

0.374

20553

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

[[_3rd_order, _missing_y]]

0.228

20558

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

[[_3rd_order, _missing_y]]

0.286

20580

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

[[_high_order, _missing_y]]

0.450

20581

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

[[_high_order, _missing_y]]

0.460

20592

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

[[_high_order, _quadrature]]

0.240

20602

\begin{align*} \left (x^{3}-4 x \right ) y^{\prime \prime \prime }+\left (9 x^{2}-4\right ) y^{\prime \prime }+18 y^{\prime } x +6 y&=6 \\ \end{align*}

[[_3rd_order, _fully, _exact, _linear]]

0.269

20761

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

[[_3rd_order, _missing_y]]

0.250

20762

\begin{align*} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 y^{\prime } x +4 y&=\frac {2}{x^{3}} \\ \end{align*}

[[_3rd_order, _fully, _exact, _linear]]

0.325

20763

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

[[_3rd_order, _fully, _exact, _linear]]

0.293

22494

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

[[_3rd_order, _missing_y]]

0.060

22498

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

[[_3rd_order, _missing_y]]

0.056

22795

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

[[_3rd_order, _missing_y]]

0.215

23398

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

[[_high_order, _missing_y]]

0.226

23474

\begin{align*} 3 x y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }&=3 \cos \left (x \right ) \\ \end{align*}

[[_3rd_order, _missing_y]]

1.006