3.1.66 Problems 6501 to 6600

Table 3.131: First order ode

#

ODE

Mathematica

Maple

14323

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

14324

\[ {}2 t y \,{\mathrm e}^{t^{2}}+2 t \,{\mathrm e}^{-y}+\left ({\mathrm e}^{t^{2}}-t^{2} {\mathrm e}^{-y}+1\right ) y^{\prime } = 0 \]

14325

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

14326

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

14327

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

14328

\[ {}\frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime } = 0 \]

14329

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

14330

\[ {}-4 x^{3}+6 y \sin \left (6 x y\right )+\left (4 y^{3}+6 x \sin \left (6 x y\right )\right ) y^{\prime } = 0 \]

14331

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

14332

\[ {}y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime } = 0 \]

14333

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

14334

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

14335

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

14336

\[ {}5 t y+4 y^{2}+1+\left (t^{2}+2 t y\right ) y^{\prime } = 0 \]

14337

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

14338

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

14339

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

14340

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

14341

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

14342

\[ {}\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime } = 0 \]

14343

\[ {}2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime } = 0 \]

14344

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

14345

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

14346

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

14347

\[ {}t y^{\prime }-y = t y^{3} \sin \left (t \right ) \]

14348

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

14349

\[ {}y^{\prime }+3 y = \sqrt {y}\, \sin \left (t \right ) \]

14350

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

14351

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

14352

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

14353

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

14354

\[ {}\cos \left (\frac {t}{t +y}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime } = 0 \]

14355

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

14356

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

14357

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

14358

\[ {}\frac {\sin \left (2 t \right )}{\cos \left (2 y\right )}+\frac {\ln \left (y\right ) y^{\prime }}{\ln \left (t \right )} = 0 \]

14359

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

14360

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

14361

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

14362

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

14363

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

14364

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

14365

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

14366

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

14367

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

14368

\[ {}2 t^{2}-7 t y+5 y^{2}+t y y^{\prime } = 0 \]

14369

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

14370

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

14371

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

14372

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

14373

\[ {}t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2} = 0 \]

14374

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

14375

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

14376

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

14377

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

14378

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

14379

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

14380

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

14381

\[ {}t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime } = 0 \]

14382

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

14383

\[ {}t y^{3}-\left (t^{4}+y^{4}\right ) y^{\prime } = 0 \]

14384

\[ {}y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime } = 0 \]

14385

\[ {}t -2 y+1+\left (4 t -3 y-6\right ) y^{\prime } = 0 \]

14386

\[ {}5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime } = 0 \]

14387

\[ {}3 t -y+1-\left (6 t -2 y-3\right ) y^{\prime } = 0 \]

14388

\[ {}2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime } = 0 \]

14389

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

14390

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

14391

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

14392

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

14393

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

14394

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

14395

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

14396

\[ {}y = -t y^{\prime }+\frac {{y^{\prime }}^{5}}{5} \]

14397

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

14398

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

14399

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

14400

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

14401

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

14402

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

14403

\[ {}y^{\prime } = \frac {2 t^{5}}{5 y^{2}} \]

14404

\[ {}\cos \left (4 x \right )-8 \sin \left (y\right ) y^{\prime } = 0 \]

14405

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

14406

\[ {}y^{\prime } = \frac {{\mathrm e}^{8 y}}{t} \]

14407

\[ {}y^{\prime } = \frac {{\mathrm e}^{5 t}}{y^{4}} \]

14408

\[ {}-\frac {1}{x^{5}}+\frac {1}{x^{3}} = \left (2 y^{4}-6 y^{9}\right ) y^{\prime } \]

14409

\[ {}y^{\prime } = \frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )} \]

14410

\[ {}y^{\prime } = \frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (-1+x \right ) \left (2 x -5\right )} \]

14411

\[ {}y^{\prime }+3 y = -10 \sin \left (t \right ) \]

14412

\[ {}3 t +\left (t -4 y\right ) y^{\prime } = 0 \]

14413

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

14414

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

14415

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

14416

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

14417

\[ {}x^{\prime } = \frac {5 t x}{x^{2}+t^{2}} \]

14418

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

14419

\[ {}t^{2} y+\sin \left (t \right )+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime } = 0 \]

14420

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

14421

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

14422

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