2.54 Problems 5301 to 5400

Table 2.54: Main lookup table

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ODE

Mathematica result

Maple result

5301

\[ {}4 x^{2} y^{\prime \prime }-4 x \,{\mathrm e}^{x} y^{\prime }+3 y \cos \relax (x ) = 0 \]

5302

\[ {}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+3 \left (x^{2}+x \right ) y^{\prime }+y = 0 \]

5303

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x +1\right ) y = 0 \]

5304

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

5305

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (-x^{3}+3\right ) y = 0 \]

5306

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

5307

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

5308

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

5309

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

5310

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

5311

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

5312

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

5313

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

5314

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

5315

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

5316

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

5317

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

5318

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

5319

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

5320

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

5321

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

5322

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

5323

\[ {}y^{\prime } = \frac {2 x +3 y+1}{x -2 y-1} \]

5324

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

5325

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

5326

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

5327

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

5328

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

5329

\[ {}\cos \relax (x ) \left (\cos ^{2}\relax (y)\right )-\sin \relax (x ) \sin \left (2 y\right ) y^{\prime } = 0 \]

5330

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

5331

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

5332

\[ {}2 y \,{\mathrm e}^{2 x}+2 x \cos \relax (y)+\left ({\mathrm e}^{2 x}-x^{2} \sin \relax (y)\right ) y^{\prime } = 0 \]

5333

\[ {}3 x^{2} \ln \relax (x )+x^{2}+y+x y^{\prime } = 0 \]

5334

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

5335

\[ {}\cos \relax (x ) \cos \relax (y)-2 \sin \relax (x ) \sin \relax (y) y^{\prime } = 0 \]

5336

\[ {}5 x^{3} y^{2}+2 y+\left (3 x^{4} y+2 x \right ) y^{\prime } = 0 \]

5337

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

5338

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

5339

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

5340

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

5341

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

5342

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

5343

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

5344

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

5345

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

5346

\[ {}y^{\prime \prime }+\sin \relax (y) = 0 \]

5347

\[ {}y^{\prime \prime }+\sin \relax (y) = 0 \]

5348

\[ {}[y_{1}^{\prime }\relax (x ) = y_{1}\relax (x ), y_{2}^{\prime }\relax (x ) = y_{1}\relax (x )+y_{2}\relax (x )] \]

5349

\[ {}[y_{1}^{\prime }\relax (x ) = y_{2}\relax (x ), y_{2}^{\prime }\relax (x ) = 6 y_{1}\relax (x )+y_{2}\relax (x )] \]

5350

\[ {}[y_{1}^{\prime }\relax (x ) = y_{1}\relax (x )+y_{2}\relax (x ), y_{2}^{\prime }\relax (x ) = y_{1}\relax (x )+y_{2}\relax (x )+{\mathrm e}^{3 x}] \]

5351

\[ {}[y_{1}^{\prime }\relax (x ) = 3 y_{1}\relax (x )+x y_{3}\relax (x ), y_{2}^{\prime }\relax (x ) = y_{2}\relax (x )+x^{3} y_{3}\relax (x ), y_{3}^{\prime }\relax (x ) = 2 x y_{2}\relax (x )-y_{2}\relax (x )+{\mathrm e}^{x} y_{3}\relax (x )] \]

5352

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

5353

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

5354

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

5355

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

5356

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

5357

\[ {}y^{\prime \prime }-4 y = 0 \]

5358

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

5359

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

5360

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

5361

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

5362

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

5363

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

5364

\[ {}\left (y \cos \relax (y)-\sin \relax (y)+x \right ) y^{\prime } = y \]

5365

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

5366

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

5367

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

5368

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

5369

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

5370

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

5371

\[ {}x y^{\prime } = 1 \]

5372

\[ {}y^{\prime } = \arcsin \relax (x ) \]

5373

\[ {}\sin \relax (x ) y^{\prime } = 1 \]

5374

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

5375

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

5376

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

5377

\[ {}y^{\prime } = 2 \sin \relax (x ) \cos \relax (x ) \]

5378

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

5379

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

5380

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

5381

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

5382

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

5383

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 0 \]

5384

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

5385

\[ {}2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y = 0 \]

5386

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

5387

\[ {}y^{\prime } = 4 x y \]

5388

\[ {}y^{\prime }+y \tan \relax (x ) = 0 \]

5389

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

5390

\[ {}y \ln \relax (y)-x y^{\prime } = 0 \]

5391

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

5392

\[ {}y^{\prime } \sin \relax (y) = x^{2} \]

5393

\[ {}y^{\prime }-y \tan \relax (x ) = 0 \]

5394

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

5395

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

5396

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

5397

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

5398

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

5399

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

5400

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