4.1.84 Problems 8301 to 8400

Table 4.167: First order ode

#

ODE

Mathematica

Maple

Sympy

20350

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

20351

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

20352

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

20353

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

20354

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

20355

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

20356

\[ {} 3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (-{\mathrm e}^{x}+1\right ) \sec \left (y\right )^{2} y^{\prime } = 0 \]

20357

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

20358

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

20359

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

20360

\[ {} 2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime } = 0 \]

20361

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

20362

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

20363

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

20364

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

20365

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

20366

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

20367

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

20368

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

20369

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

20370

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

20371

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

20372

\[ {} \left (6 x -5 y+4\right ) y^{\prime }+y-2 x -1 = 0 \]

20373

\[ {} \left (x -3 y+4\right ) y^{\prime }+7 y-5 x = 0 \]

20374

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

20375

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

20376

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

20377

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

20378

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

20379

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

20380

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

20381

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

20382

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

20383

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

20384

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

20385

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

20386

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

20387

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

20388

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

20389

\[ {} y^{\prime }+3 x^{2} y = x^{5} {\mathrm e}^{x^{3}} \]

20390

\[ {} y^{\prime }-\frac {\tan \left (y\right )}{1+x} = \left (1+x \right ) {\mathrm e}^{x} \sec \left (y\right ) \]

20391

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

20392

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

20393

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

20394

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

20395

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

20396

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

20397

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

20398

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

20399

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

20400

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

20401

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

20402

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

20403

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

20404

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

20405

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

20406

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

20407

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

20408

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

20409

\[ {} \left (20 x^{2}+8 x y+4 y^{2}+3 y^{3}\right ) y+4 \left (x^{2}+x y+y^{2}+y^{3}\right ) x y^{\prime } = 0 \]

20410

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

20411

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

20412

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

20413

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

20414

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

20415

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

20416

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

20417

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

20418

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

20419

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

20420

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

20421

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

20422

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

20423

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

20424

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

20425

\[ {} {x^{\prime }}^{2} = k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right ) \]

20426

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

20427

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

20428

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

20429

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

20430

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

20431

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

20432

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

20433

\[ {} s^{\prime }+x^{2} = x^{2} {\mathrm e}^{3 s} \]

20434

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

20435

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

20436

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

20437

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

20438

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

20439

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

20440

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

20441

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

20442

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

20443

\[ {} y^{\prime }+\frac {a x +b y+c}{b x +f y+e} = 0 \]

20496

\[ {} {y^{\prime }}^{2}-7 y^{\prime }+12 = 0 \]

20497

\[ {} {y^{\prime }}^{2}-5 y^{\prime }+6 = 0 \]

20498

\[ {} {y^{\prime }}^{2}-9 y^{\prime }+18 = 0 \]

20499

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

20500

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

20501

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