4.1.33 Problems 3201 to 3300

Table 4.65: First order ode

#

ODE

Mathematica

Maple

Sympy

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

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

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

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

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

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

6515

\[ {} y^{\prime }-5 y = \left (x -1\right ) \sin \left (x \right )+\left (1+x \right ) \cos \left (x \right ) \]

6516

\[ {} y^{\prime }-5 y = 3 \,{\mathrm e}^{x}-2 x +1 \]

6517

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

6523

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

6524

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

6525

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

6533

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

6542

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

6543

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

6544

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

6545

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

6569

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

6570

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

6571

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

6572

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

6579

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

6580

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

6581

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

6582

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

6583

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

6584

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

6585

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

6586

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

6587

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

6588

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

6589

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

6590

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

6591

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

6592

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

6593

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

6594

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

6595

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

6596

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

6597

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

6598

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

6599

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

6600

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

6601

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

6602

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

6603

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

6604

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

6605

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

6606

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

6607

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

6608

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

6609

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

6610

\[ {} 2 u^{2}+2 u v+\left (u^{2}+v^{2}\right ) v^{\prime } = 0 \]

6611

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

6612

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

6613

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

6614

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

6615

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

6616

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

6617

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

6618

\[ {} 1-\sqrt {a^{2}-x^{2}}\, y^{\prime } = 0 \]

6619

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

6620

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

6621

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

6622

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