4.24.44 Problems 4301 to 4400

Table 4.1439: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

17900

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 8 x \]

17909

\[ {} t \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )+y y^{\prime } = 1 \]

18194

\[ {} x y^{\prime \prime \prime } = 2 \]

18195

\[ {} y^{\prime \prime } = {y^{\prime }}^{2} \]

18196

\[ {} \left (x -1\right ) y^{\prime \prime } = 1 \]

18200

\[ {} y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \]

18201

\[ {} y y^{\prime \prime }+{y^{\prime }}^{2} = 1 \]

18204

\[ {} y^{\prime \prime } \left (x +2\right )^{5} = 1 \]

18207

\[ {} x y^{\prime \prime } = y^{\prime } \]

18208

\[ {} x y^{\prime \prime }+y^{\prime } = 0 \]

18209

\[ {} x y^{\prime \prime } = \left (2 x^{2}+1\right ) y^{\prime } \]

18210

\[ {} x y^{\prime \prime } = y^{\prime }+x^{2} \]

18211

\[ {} x \ln \left (x \right ) y^{\prime \prime } = y^{\prime } \]

18213

\[ {} 2 y^{\prime \prime } = \frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }} \]

18214

\[ {} y^{\prime \prime \prime } = \sqrt {1-{y^{\prime \prime }}^{2}} \]

18215

\[ {} x y^{\prime \prime \prime }-y^{\prime \prime } = 0 \]

18216

\[ {} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \]

18217

\[ {} y^{\prime \prime } = {y^{\prime }}^{2} \]

18218

\[ {} y^{\prime \prime } = \sqrt {1-{y^{\prime }}^{2}} \]

18219

\[ {} y^{\prime \prime } = 1+{y^{\prime }}^{2} \]

18220

\[ {} y^{\prime \prime } = \sqrt {1+y^{\prime }} \]

18221

\[ {} y^{\prime \prime } = y^{\prime } \ln \left (y^{\prime }\right ) \]

18223

\[ {} y^{\prime \prime } = y^{\prime } \left (1+y^{\prime }\right ) \]

18224

\[ {} 3 y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \]

18225

\[ {} y^{\prime \prime \prime }+{y^{\prime \prime }}^{2} = 0 \]

18226

\[ {} y y^{\prime \prime } = {y^{\prime }}^{2} \]

18227

\[ {} y^{\prime \prime } = 2 y y^{\prime } \]

18228

\[ {} 3 y^{\prime } y^{\prime \prime } = 2 y \]

18229

\[ {} 2 y^{\prime \prime } = 3 y^{2} \]

18230

\[ {} y y^{\prime \prime }+{y^{\prime }}^{2} = 0 \]

18231

\[ {} y y^{\prime \prime } = {y^{\prime }}^{2}+y^{\prime } \]

18232

\[ {} y y^{\prime \prime } = 1+{y^{\prime }}^{2} \]

18233

\[ {} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2} \]

18234

\[ {} y^{3} y^{\prime \prime } = -1 \]

18235

\[ {} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} y^{\prime } \]

18236

\[ {} y^{\prime \prime } = {\mathrm e}^{2 y} \]

18237

\[ {} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2} = 4 y^{2} \]

18238

\[ {} y^{\prime \prime \prime } = 3 y y^{\prime } \]

18404

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

18405

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

18406

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }+6 y = 0 \]

18407

\[ {} x y^{\prime \prime }+y^{\prime } = 0 \]

18408

\[ {} \left (x +2\right )^{2} y^{\prime \prime }+3 \left (x +2\right ) y^{\prime }-3 y = 0 \]

18409

\[ {} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y = 0 \]

18410

\[ {} x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime } = 0 \]

18411

\[ {} x^{2} y^{\prime \prime \prime } = 2 y^{\prime } \]

18412

\[ {} \left (1+x \right )^{2} y^{\prime \prime \prime }-12 y^{\prime } = 0 \]

18413

\[ {} \left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } = 0 \]

18414

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+y = x \left (6-\ln \left (x \right )\right ) \]

18415

\[ {} x^{2} y^{\prime \prime }-2 y = \sin \left (\ln \left (x \right )\right ) \]

18416

\[ {} x^{2} y^{\prime \prime }-x y^{\prime }-3 y = -\frac {16 \ln \left (x \right )}{x} \]

18417

\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y = x^{2}-2 x +2 \]

18418

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m} \]

18419

\[ {} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 \ln \left (x \right )^{2}+12 x \]

18420

\[ {} \left (1+x \right )^{3} y^{\prime \prime }+3 \left (1+x \right )^{2} y^{\prime }+\left (1+x \right ) y = 6 \ln \left (1+x \right ) \]

18421

\[ {} \left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y = x \]

18422

\[ {} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0 \]

18423

\[ {} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y = 0 \]

18424

\[ {} \left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 y^{\prime } \left (1+x \right )+6 y = 6 \]

18425

\[ {} x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \]

18426

\[ {} y^{\prime \prime }+\left (\tan \left (x \right )-2 \cot \left (x \right )\right ) y^{\prime }+2 \cot \left (x \right )^{2} y = 0 \]

18427

\[ {} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2} = 0 \]

18428

\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = 1 \]

18429

\[ {} x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 5 x^{4} \]

18430

\[ {} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = \left (x -1\right )^{2} {\mathrm e}^{x} \]

18431

\[ {} y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-2 x} = {\mathrm e}^{-3 x} \]

18432

\[ {} \left (x^{4}-x^{3}\right ) y^{\prime \prime }+\left (2 x^{3}-2 x^{2}-x \right ) y^{\prime }-y = \frac {\left (x -1\right )^{2}}{x} \]

18433

\[ {} y^{\prime \prime }-y^{\prime }+y \,{\mathrm e}^{2 x} = x \,{\mathrm e}^{2 x}-1 \]

18434

\[ {} x \left (x -1\right ) y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y = x^{2} \left (2 x -3\right ) \]

18444

\[ {} x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime } = 4 x^{3} {\mathrm e}^{x^{2}} \]

18445

\[ {} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime } = 1 \]

18446

\[ {} x \ln \left (x \right ) y^{\prime \prime }-y^{\prime } = \ln \left (x \right )^{2} \]

18447

\[ {} x y^{\prime \prime }+\left (2 x -1\right ) y^{\prime } = -4 x^{2} \]

18448

\[ {} y^{\prime \prime }+\tan \left (x \right ) y^{\prime } = \cos \left (x \right ) \cot \left (x \right ) \]

18449

\[ {} 4 x y^{\prime \prime }+2 y^{\prime }+y = 1 \]

18450

\[ {} 4 x y^{\prime \prime }+2 y^{\prime }+y = \frac {x +6}{x^{2}} \]

18451

\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {1}{x^{2}+1} \]

18452

\[ {} -y+x y^{\prime }+\left (1-x \right ) y^{\prime \prime } = \left (x -1\right )^{2} {\mathrm e}^{x} \]

18453

\[ {} 2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y = \frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}} \]

18454

\[ {} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y = 4 \,{\mathrm e}^{x} \]

18455

\[ {} x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x^{2} y^{\prime }+x y = 2 \ln \left (x \right ) \]

18456

\[ {} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-2 \left (1-x \right ) y = -2+2 x \]

18460

\[ {} x^{\prime \prime }+{x^{\prime }}^{2}+x = 0 \]

18461

\[ {} x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x = 0 \]

18462

\[ {} x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }} = 0 \]

18463

\[ {} x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x = 0 \]

18464

\[ {} x^{\prime \prime }+x {x^{\prime }}^{2} = 0 \]

18465

\[ {} x^{\prime \prime }+\left (x+2\right ) x^{\prime } = 0 \]

18466

\[ {} x^{\prime \prime }-x^{\prime }+x-x^{2} = 0 \]

18471

\[ {} 1+{y^{\prime }}^{2}+y y^{\prime \prime } = 0 \]

18482

\[ {} x y^{\prime \prime }+y^{\prime } = 0 \]

18483

\[ {} 2 y^{\prime \prime }+4 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime } = 0 \]

18484

\[ {} 6 x y^{\prime \prime }+6 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime } = 0 \]

18503

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x^{2}-\frac {1}{9}\right ) y = 0 \]

18504

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

18505

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{9} = 0 \]

18506

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{x}+4 y = 0 \]

18507

\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }+4 \left (x^{4}-1\right ) y = 0 \]

18508

\[ {} x y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{4} = 0 \]

18509

\[ {} y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y = 0 \]