6.65 Problems 6401 to 6500

Table 6.129: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

6401

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

6402

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

6403

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

6404

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

6405

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

6406

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

6407

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

6408

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

6409

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

6410

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

6411

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

6412

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

6413

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

6414

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

6415

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

6416

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

6417

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

6418

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

6419

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

6420

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

6421

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

6422

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

6423

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

6424

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

6425

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

6426

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

6427

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

6428

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

6429

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

6430

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

6431

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

6432

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

6433

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

6434

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

6435

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

6436

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

6437

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

6438

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

6439

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

6440

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

6441

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

6442

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

6443

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

6444

\[ {} y^{\prime }+\cot \left (x \right ) y = 5 \,{\mathrm e}^{\cos \left (x \right )} \]

6445

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

6446

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

6447

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

6448

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

6449

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

6450

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

6451

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

6452

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

6453

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

6454

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

6455

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

6456

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

6457

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

6458

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

6459

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

6460

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

6461

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

6462

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

6463

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

6464

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

6465

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

6466

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

6467

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

6468

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

6469

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

6470

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

6471

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

6472

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

6473

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

6474

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

6475

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

6476

\[ {} \frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}} = 1 \]

6477

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

6478

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

6479

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 8 \]

6480

\[ {} y^{\prime \prime }-4 y = 10 \,{\mathrm e}^{3 x} \]

6481

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

6482

\[ {} y^{\prime \prime }+25 y = 5 x^{2}+x \]

6483

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

6484

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x} \]

6485

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

6486

\[ {} y^{\prime \prime }-6 y^{\prime }+8 y = 8 \,{\mathrm e}^{4 x} \]

6487

\[ {} 2 y^{\prime \prime }-7 y^{\prime }-4 y = {\mathrm e}^{3 x} \]

6488

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 54 x +18 \]

6489

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 100 \sin \left (4 x \right ) \]

6490

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

6491

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

6492

\[ {} y^{\prime \prime }-y^{\prime }+10 y = 20-{\mathrm e}^{2 x} \]

6493

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

6494

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

6495

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

6496

\[ {} y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (x \right ) \]

6497

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

6498

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = 6 \sin \left (t \right ) \]

6499

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

6500

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