3.9.22 Problems 2101 to 2200

Table 3.549: First order ode linear in derivative

#

ODE

Mathematica

Maple

4428

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

4429

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

4430

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

4431

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

4432

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

4433

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

4434

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

4435

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

4436

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

4437

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

4438

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

4439

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

4440

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

4441

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

4442

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

4443

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

4444

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

4445

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

4446

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

4447

\[ {}7 y-3+\left (2 x +1\right ) y^{\prime } = 0 \]

4448

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

4449

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

4450

\[ {}3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime } = 0 \]

4451

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

4452

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

4453

\[ {}y+7+\left (2 x +y+3\right ) y^{\prime } = 0 \]

4454

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

4455

\[ {}3 x^{2} y+8 x y^{2}+\left (x^{3}+8 x^{2} y+12 y^{2}\right ) y^{\prime } = 0 \]

4456

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

4457

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

4458

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

4459

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

4460

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

4461

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

4462

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

4463

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

4464

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

4465

\[ {}{\mathrm e}^{x} \left (y^{3}+x y^{3}+1\right )+3 y^{2} \left (x \,{\mathrm e}^{x}-6\right ) y^{\prime } = 0 \]

4466

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

4467

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

4468

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

4469

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

4470

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

4471

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

4472

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

4473

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

4474

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

4475

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

4476

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

4477

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

4478

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

4479

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

4480

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

4481

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

4482

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

4483

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

4484

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

4485

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

4486

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

4487

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

4488

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

4489

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

4490

\[ {}y^{2}+12 x^{2} y+\left (2 x y+4 x^{3}\right ) y^{\prime } = 0 \]

4491

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

4492

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

4493

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

4494

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

4495

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

4496

\[ {}y^{\prime }+a y = b \]

4497

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

4498

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

4499

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

4500

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

4501

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

4502

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

4503

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

4504

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

4505

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

4506

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

4507

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

4508

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

4509

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

4510

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

4511

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

4512

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

4513

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

4514

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

4515

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

4516

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

4517

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

4518

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

4519

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

4520

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

4521

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

4522

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

4523

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

4524

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

4525

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

4526

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

4527

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