6.144 Problems 14301 to 14400

Table 6.287: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

14301

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

14302

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

14303

\[ {} y^{\prime }+8 x y^{\prime \prime }+4 x^{2} y^{\prime \prime \prime } = 0 \]

14304

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

14305

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

14306

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

14307

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

14308

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

14309

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

14310

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

14311

\[ {} x^{\prime }+2 x = t^{2}+4 t +7 \]

14312

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

14313

\[ {} t^{2} x^{\prime \prime }-6 x = 0 \]

14314

\[ {} 2 x^{\prime \prime }-5 x^{\prime }-3 x = 0 \]

14315

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

14316

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

14317

\[ {} x^{\prime } = t \cos \left (t^{2}\right ) \]

14318

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

14319

\[ {} x^{\prime \prime } = -3 \sqrt {t} \]

14320

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

14321

\[ {} x^{\prime } = \frac {1}{t \ln \left (t \right )} \]

14322

\[ {} \sqrt {t}\, x^{\prime } = \cos \left (\sqrt {t}\right ) \]

14323

\[ {} x^{\prime } = \frac {{\mathrm e}^{-t}}{\sqrt {t}} \]

14324

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

14325

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

14326

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

14327

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

14328

\[ {} u^{\prime } = \frac {1}{5-2 u} \]

14329

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

14330

\[ {} Q^{\prime } = \frac {Q}{4+Q^{2}} \]

14331

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

14332

\[ {} y^{\prime } = r \left (a -y\right ) \]

14333

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

14334

\[ {} \theta ^{\prime } = t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \]

14335

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

14336

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

14337

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

14338

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

14339

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

14340

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

14341

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

14342

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

14343

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

14344

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

14345

\[ {} T^{\prime } = 2 a t \left (T^{2}-a^{2}\right ) \]

14346

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

14347

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

14348

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

14349

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

14350

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

14351

\[ {} x^{\prime } = \frac {4 t^{2}+3 x^{2}}{2 t x} \]

14352

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

14353

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

14354

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

14355

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

14356

\[ {} x^{\prime } = 2 t^{3} x-6 \]

14357

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

14358

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

14359

\[ {} 7 t^{2} x^{\prime } = 3 x-2 t \]

14360

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

14361

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

14362

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

14363

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

14364

\[ {} x^{\prime }+2 t x = {\mathrm e}^{-t^{2}} \]

14365

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

14366

\[ {} \theta ^{\prime } = -a \theta +{\mathrm e}^{b t} \]

14367

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

14368

\[ {} x^{\prime }+\frac {5 x}{t} = t +1 \]

14369

\[ {} x^{\prime } = \left (a +\frac {b}{t}\right ) x \]

14370

\[ {} R^{\prime }+\frac {R}{t} = \frac {2}{t^{2}+1} \]

14371

\[ {} N^{\prime } = N-9 \,{\mathrm e}^{-t} \]

14372

\[ {} \cos \left (\theta \right ) v^{\prime }+v = 3 \]

14373

\[ {} R^{\prime } = \frac {R}{t}+t \,{\mathrm e}^{-t} \]

14374

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

14375

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

14376

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

14377

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

14378

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

14379

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

14380

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

14381

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

14382

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

14383

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

14384

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

14385

\[ {} x^{\prime } = a x+b x^{3} \]

14386

\[ {} w^{\prime } = t w+t^{3} w^{3} \]

14387

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

14388

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

14389

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

14390

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

14391

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

14392

\[ {} t \cot \left (x\right ) x^{\prime } = -2 \]

14393

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

14394

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

14395

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

14396

\[ {} x^{\prime \prime }+4 x^{\prime }+3 x = 0 \]

14397

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

14398

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

14399

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

14400

\[ {} x^{\prime \prime }+4 x^{\prime }+3 x = 0 \]