3.1.27 Problems 2601 to 2700

Table 3.53: First order ode

#

ODE

Mathematica

Maple

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

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

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

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

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

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

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

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

4528

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

4529

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

4530

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

4531

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

4532

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

4533

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

4534

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

4535

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

4536

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

4537

\[ {}y^{\prime }+a y = k \,{\mathrm e}^{b x} \]

4538

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

4539

\[ {}y^{\prime }+8 y^{3} x^{3}+2 x y = 0 \]

4540

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

4541

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

4542

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

4543

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

4544

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

4545

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

4546

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

4547

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

4548

\[ {}x y^{\prime }+a y+b \,x^{n} = 0 \]

4549

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

4550

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

4551

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

4552

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

4553

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

4554

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

4555

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

4556

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

4557

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

4558

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

4559

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

4560

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

4561

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

4562

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

4563

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

4564

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

4565

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

4566

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

4567

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

4568

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

4569

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

4570

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

4571

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

4675

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

4676

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

4677

\[ {}y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-1-a} = 0 \]

4678

\[ {}y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )} = 0 \]

4679

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

4680

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

4681

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