4.145 Problems 14401 to 14500

Table 4.289: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

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

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

14423

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

14424

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

14425

\[ {}t r^{\prime }+r = t \cos \left (t \right ) \]

14426

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

14427

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

14428

\[ {}y = t y^{\prime }+3 {y^{\prime }}^{4} \]

14429

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

14430

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

14431

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

14432

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

14433

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

14434

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

14435

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

14436

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

14437

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

14438

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

14439

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

14440

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

14441

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

14442

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

14443

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

14444

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

14445

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

14446

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

14447

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

14448

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

14449

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

14450

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

14451

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

14452

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

14453

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

14454

\[ {}y^{\prime \prime }+10 y^{\prime }+24 y = 0 \]

14455

\[ {}y^{\prime \prime }+16 y = 0 \]

14456

\[ {}y^{\prime \prime }+6 y^{\prime }+18 y = 0 \]

14457

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

14458

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

14459

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 0 \]

14460

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

14461

\[ {}y^{\prime \prime }+10 y^{\prime }+25 y = 0 \]

14462

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

14463

\[ {}y^{\prime \prime }+49 y = 0 \]

14464

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

14465

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

14466

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

14467

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

14468

\[ {}a y^{\prime \prime }+b y^{\prime }+c y = 0 \]

14469

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

14470

\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (36 t^{2}-1\right ) y = 0 \]

14471

\[ {}t y^{\prime \prime }+2 y^{\prime }+16 t y = 0 \]

14472

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

14473

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

14474

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

14475

\[ {}y^{\prime \prime }-4 y^{\prime }-12 y = 0 \]

14476

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

14477

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

14478

\[ {}y^{\prime \prime }+8 y^{\prime }+12 y = 0 \]

14479

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

14480

\[ {}8 y^{\prime \prime }+6 y^{\prime }+y = 0 \]

14481

\[ {}4 y^{\prime \prime }+9 y = 0 \]

14482

\[ {}y^{\prime \prime }+16 y = 0 \]

14483

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

14484

\[ {}y^{\prime \prime }+7 y = 0 \]

14485

\[ {}4 y^{\prime \prime }+21 y^{\prime }+5 y = 0 \]

14486

\[ {}7 y^{\prime \prime }+4 y^{\prime }-3 y = 0 \]

14487

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

14488

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]

14489

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

14490

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

14491

\[ {}y^{\prime \prime }+y^{\prime }-12 y = 0 \]

14492

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = 0 \]

14493

\[ {}2 y^{\prime \prime }-7 y^{\prime }-4 y = 0 \]

14494

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \]

14495

\[ {}y^{\prime \prime }+36 y = 0 \]

14496

\[ {}y^{\prime \prime }+100 y = 0 \]

14497

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

14498

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

14499

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

14500

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 0 \]