2.7.3 higher order ode exact

Table 2.1253: higher order ode exact [104]

#

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]]

0.262

3498

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

[[_3rd_order, _missing_y]]

0.250

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]]

1.128

6670

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

[[_3rd_order, _quadrature]]

0.630

6676

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

[[_3rd_order, _fully, _exact, _linear]]

0.960

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]]

1.385

6679

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

[[_3rd_order, _missing_y]]

0.300

6681

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

[[_3rd_order, _missing_y]]

0.644

6682

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

[[_3rd_order, _missing_y]]

0.487

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]]

0.872

6689

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

[[_3rd_order, _missing_y]]

0.986

6690

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

[[_3rd_order, _missing_y]]

0.589

6709

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

[[_3rd_order, _fully, _exact, _linear]]

0.710

6711

\begin{align*} -4 y-14 x y^{\prime }+\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]]

0.816

6724

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

[[_3rd_order, _fully, _exact, _linear]]

0.835

6762

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

[[_high_order, _missing_y]]

1.010

6763

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

[[_high_order, _missing_y]]

1.039

6764

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

[[_high_order, _missing_y]]

3.644

6765

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

[[_high_order, _missing_y]]

0.658

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]]

0.267

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]]

0.588

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]]

0.569

6770

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

[[_high_order, _quadrature]]

0.899

6773

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

[[_high_order, _missing_y]]

0.780

6781

\begin{align*} y \,{\mathrm e}^{x}+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]]

0.865

8188

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

[[_3rd_order, _missing_y]]

0.294

9313

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

[[_high_order, _missing_y]]

0.510

9846

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

[[_3rd_order, _exact, _linear, _homogeneous]]

2.620

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]]

0.243

12732

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

[[_3rd_order, _fully, _exact, _linear]]

0.229

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]]

0.462

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]]

0.205

12745

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

[[_3rd_order, _missing_y]]

0.231

12746

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

[[_3rd_order, _missing_y]]

0.209

12754

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

[[_3rd_order, _missing_y]]

0.208

12777

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

[[_3rd_order, _missing_y]]

0.422

12778

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

[[_3rd_order, _fully, _exact, _linear]]

0.280

12793

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

[[_high_order, _missing_y]]

0.210

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]]

0.087

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]]

0.243

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]]

0.243

12804

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

[[_high_order, _missing_y]]

0.272

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 }+y \,{\mathrm e}^{x}-\frac {1}{x^{5}}&=0 \\ \end{align*}

[[_high_order, _fully, _exact, _linear]]

0.341

14167

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

[[_3rd_order, _missing_y]]

0.863

14170

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

[[_3rd_order, _fully, _exact, _linear]]

0.650

14182

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

[[_3rd_order, _fully, _exact, _linear]]

0.474

14189

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

[[_3rd_order, _missing_y]]

0.423

15400

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

[[_3rd_order, _quadrature]]

0.529

16398

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

[[_3rd_order, _missing_y]]

0.277

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]]

0.309

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]]

0.262

17632

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

[[_high_order, _missing_y]]

0.444

18080

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

[[_3rd_order, _quadrature]]

0.461

18101

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

[[_3rd_order, _missing_y]]

0.407

18296

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

[[_3rd_order, _missing_y]]

0.355

18297

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

[[_3rd_order, _missing_y]]

0.341

18298

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

[[_3rd_order, _missing_y]]

0.466

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]]

0.702

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]]

0.254

18370

\begin{align*} 6 x y^{\prime \prime }+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]]

0.522

18984

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

[[_3rd_order, _missing_y]]

0.632

19171

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

[[_3rd_order, _missing_y]]

0.484

19550

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

[[_high_order, _missing_y]]

0.381

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]]

0.320

19866

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

[[_3rd_order, _missing_y]]

0.288

20116

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

[[_3rd_order, _fully, _exact, _linear]]

0.350

20124

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

[[_high_order, _quadrature]]

0.286

20130

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

[[_3rd_order, _missing_y]]

0.252

20140

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

[[_high_order, _missing_y]]

0.658

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]]

0.415

20157

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

[[_3rd_order, _fully, _exact, _linear]]

0.352

20161

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

[[_3rd_order, _missing_y]]

0.270

20166

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

[[_3rd_order, _fully, _exact, _linear]]

0.431

20487

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

[[_3rd_order, _missing_y]]

0.274

20490

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

[[_3rd_order, _missing_y]]

0.279

20493

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

[[_3rd_order, _missing_y]]

0.359

20504

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

[[_3rd_order, _missing_y]]

0.475

20520

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

[[_3rd_order, _fully, _exact, _linear]]

0.366

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]]

0.535

20553

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

[[_3rd_order, _missing_y]]

0.300

20558

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

[[_3rd_order, _missing_y]]

0.287

20580

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

[[_high_order, _missing_y]]

0.657

20581

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

[[_high_order, _missing_y]]

0.563

20592

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

[[_high_order, _quadrature]]

0.347

20602

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

[[_3rd_order, _fully, _exact, _linear]]

0.323

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]]

0.293

20762

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

[[_3rd_order, _fully, _exact, _linear]]

0.362

20763

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

[[_3rd_order, _fully, _exact, _linear]]

0.260

22494

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

[[_3rd_order, _missing_y]]

0.150

22498

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

[[_3rd_order, _missing_y]]

0.156

22795

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

[[_3rd_order, _missing_y]]

0.490

23398

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

[[_high_order, _missing_y]]

0.337

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]]

1.139

26417

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

[[_3rd_order, _quadrature]]

0.237

26457

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

[[_3rd_order, _missing_y]]

0.084

26462

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

[[_3rd_order, _missing_y]]

0.286

26622

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

[[_3rd_order, _missing_y]]

0.293

26623

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

[[_3rd_order, _missing_y]]

0.342

26624

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

[[_3rd_order, _missing_y]]

0.586

27556

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

[[_high_order, _quadrature]]

0.223

27558

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

[[_3rd_order, _missing_y]]

0.564

27559

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

[[_high_order, _missing_y]]

0.246

27693

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

[[_3rd_order, _missing_y]]

0.189

27721

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

[[_3rd_order, _exact, _linear, _homogeneous]]

0.463