4.9.28 Problems 2701 to 2800

Table 4.679: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

6335

\[ {} \cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta } = 0 \]

6336

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

6337

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

6338

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

6339

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

6340

\[ {} y^{\prime }-4 y = 32 x^{2} \]

6341

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

6342

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

6343

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

6344

\[ {} t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}} = 0 \]

6398

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

6399

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

6400

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

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

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

6415

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

6416

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

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

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

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

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

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

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

6454

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

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

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

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

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

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

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

6572

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

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

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