6.165 Problems 16401 to 16500

Table 6.329: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

16401

\[ {} \cos \left (-4 y+8 x -3\right ) y^{\prime } = 2+2 \cos \left (-4 y+8 x -3\right ) \]

16402

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

16403

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

16404

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

16405

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

16406

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

16407

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

16408

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

16409

\[ {} y^{\prime }+3 y \cot \left (x \right ) = 6 \cos \left (x \right ) y^{{2}/{3}} \]

16410

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

16411

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

16412

\[ {} 3 y^{\prime } = -2+\sqrt {2 x +3 y+4} \]

16413

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

16414

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

16415

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

16416

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

16417

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

16418

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

16419

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

16420

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

16421

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

16422

\[ {} y^{\prime }+3 y = \frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \]

16423

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

16424

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

16425

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

16426

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

16427

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

16428

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

16429

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

16430

\[ {} 2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime } = 0 \]

16431

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

16432

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

16433

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

16434

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

16435

\[ {} 1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime } = 0 \]

16436

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

16437

\[ {} 1+y^{4}+x y^{3} y^{\prime } = 0 \]

16438

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

16439

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

16440

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

16441

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

16442

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

16443

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

16444

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

16445

\[ {} 6+12 x^{2} y^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime } = 0 \]

16446

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

16447

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

16448

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

16449

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

16450

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

16451

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

16452

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

16453

\[ {} 4 x y-6+x^{2} y^{\prime } = 0 \]

16454

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

16455

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

16456

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

16457

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

16458

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

16459

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

16460

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

16461

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

16462

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

16463

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

16464

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

16465

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

16466

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

16467

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

16468

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

16469

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

16470

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

16471

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

16472

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

16473

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

16474

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

16475

\[ {} y^{\prime }-3 y = 12 \,{\mathrm e}^{2 x} \]

16476

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

16477

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

16478

\[ {} x y^{3} y^{\prime } = y^{4}-x^{2} \]

16479

\[ {} y^{\prime } = 4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \]

16480

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

16481

\[ {} x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime } = 0 \]

16482

\[ {} y y^{\prime }-x y^{2} = 6 x \,{\mathrm e}^{4 x^{2}} \]

16483

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

16484

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

16485

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

16486

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

16487

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

16488

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

16489

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

16490

\[ {} y^{\prime } = {\mathrm e}^{4 x +3 y} \]

16491

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

16492

\[ {} y^{\prime } = {\mathrm e}^{4 x +3 y} \]

16493

\[ {} y^{\prime } = x \left (6 y+{\mathrm e}^{x^{2}}\right ) \]

16494

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

16495

\[ {} x^{2} y^{\prime }+3 x y = 6 \,{\mathrm e}^{-x^{2}} \]

16496

\[ {} x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

16497

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

16498

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

16499

\[ {} y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x} \]

16500

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