6.205 Problems 20401 to 20500

Table 6.409: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

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

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

20444

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

20445

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

20446

\[ {} 2 x^{\prime \prime }+5 x^{\prime }-12 x = 0 \]

20447

\[ {} y^{\prime \prime }+3 y^{\prime }-54 y = 0 \]

20448

\[ {} 9 x^{\prime \prime }+18 x^{\prime }-16 x = 0 \]

20449

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

20450

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

20451

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

20452

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

20453

\[ {} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y = 0 \]

20454

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

20455

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

20456

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

20457

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

20458

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{4 x} \]

20459

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

20460

\[ {} y^{\prime \prime }+2 y^{\prime }-15 y = 15 x^{2} \]

20461

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

20462

\[ {} y-2 y^{\prime }+y^{\prime \prime } = 2 \,{\mathrm e}^{\frac {5 x}{2}} \]

20463

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

20464

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

20465

\[ {} y^{\prime \prime }+9 y = \sin \left (2 x \right )+\cos \left (2 x \right ) \]

20466

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

20467

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

20468

\[ {} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-12 y = \cos \left (4 x \right ) \]

20469

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

20470

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

20471

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 = 0 \]

20472

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

20473

\[ {} y^{\prime \prime \prime }-y^{\prime \prime }-6 y^{\prime } = x^{2}+1 \]

20474

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

20475

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

20476

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{2 x} \sin \left (x \right ) \]

20477

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

20478

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

20479

\[ {} y^{\prime \prime \prime }-7 y^{\prime }-6 y = {\mathrm e}^{2 x} \left (1+x \right ) \]

20480

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

20481

\[ {} y^{\prime \prime }+4 y^{\prime }-12 y = \left (x -1\right ) {\mathrm e}^{2 x} \]

20482

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

20483

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

20484

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

20485

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

20486

\[ {} 4 y-4 y^{\prime }+y^{\prime \prime } = 8 x^{2} {\mathrm e}^{2 x} \sin \left (2 x \right ) \]

20487

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

20488

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

20489

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

20490

\[ {} y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y = 16 x^{2}+256 \]

20491

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

20492

\[ {} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = 96 \sin \left (2 x \right ) \cos \left (x \right ) \]

20493

\[ {} y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y = 0 \]

20494

\[ {} y^{\prime \prime }+2 y^{\prime }+10 y+37 \sin \left (3 x \right ) = 0 \]

20495

\[ {} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime } = 24 x \cos \left (x \right ) \]

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

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