6.195 Problems 19401 to 19500

Table 6.389: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

19401

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

19402

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

19403

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

19404

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

19405

\[ {} y^{\prime } = \frac {x +y-1}{x +4 y+2} \]

19406

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

19407

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

19408

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

19409

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

19410

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

19411

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

19412

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

19413

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

19414

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

19415

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

19416

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

19417

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

19418

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

19419

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

19420

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

19421

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

19422

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

19423

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

19424

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

19425

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

19426

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

19427

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

19428

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

19429

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

19430

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

19431

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

19432

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

19433

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

19434

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

19435

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

19436

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

19437

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

19438

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

19439

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

19440

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

19441

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

19442

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

19443

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

19444

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

19445

\[ {} x y^{\prime } = y+x^{2}+9 y^{2} \]

19446

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

19447

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

19448

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

19449

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

19450

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

19451

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

19452

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

19453

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

19454

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

19455

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

19456

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

19457

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

19458

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

19459

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

19460

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

19461

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

19462

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

19463

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

19464

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

19465

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

19466

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

19467

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

19468

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

19469

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

19470

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

19471

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

19472

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

19473

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

19474

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

19475

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

19476

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

19477

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

19478

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

19479

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

19480

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

19481

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

19482

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

19483

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

19484

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

19485

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

19486

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

19487

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

19488

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

19489

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

19490

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

19491

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

19492

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

19493

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

19494

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

19495

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

19496

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

19497

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

19498

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

19499

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

19500

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