2.124 Problems 12301 to 12400

Table 2.247: Main lookup table

#

ODE

Mathematica result

Maple result

12301

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

12302

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

12303

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

12304

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

12305

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

12306

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

12307

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

12308

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

12309

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

12310

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

12311

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

12312

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

12313

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

12314

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

12315

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

12316

\[ {}y^{\prime } = \frac {1}{\sqrt {15-x^{2}-y^{2}}} \]

12317

\[ {}y^{\prime } = \frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x} \]

12318

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

12319

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

12320

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

12321

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

12322

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

12323

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

12324

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

12325

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

12326

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

12327

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

12328

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

12329

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

12330

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

12331

\[ {}y^{\prime } = a y+b \]

12332

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

12333

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

12334

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

12335

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

12336

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

12337

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

12338

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

12339

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

12340

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

12341

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

12342

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

12343

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

12344

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

12345

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

12346

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

12347

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

12348

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

12349

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

12350

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

12351

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

12352

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

12353

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

12354

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

12355

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

12356

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

12357

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

12358

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

12359

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

12360

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

12361

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

12362

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

12363

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

12364

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

12365

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

12366

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

12367

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

12368

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

12369

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

12370

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

12371

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

12372

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

12373

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

12374

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

12375

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

12376

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

12377

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

12378

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

12379

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

12380

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

12381

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

12382

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

12383

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

12384

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

12385

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

12386

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

12387

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

12388

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

12389

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

12390

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

12391

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

12392

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

12393

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

12394

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

12395

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

12396

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

12397

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

12398

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

12399

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

12400

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