3.1.57 Problems 5601 to 5700

Table 3.113: First order ode

#

ODE

Mathematica

Maple

12426

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

12427

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

12428

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

12429

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

12430

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

12431

\[ {}z-\left (-a^{2}+t^{2}\right ) z^{\prime } = 0 \]

12432

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

12433

\[ {}1+s^{2}-\sqrt {t}\, s^{\prime } = 0 \]

12434

\[ {}r^{\prime }+r \tan \left (t \right ) = 0 \]

12435

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

12436

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

12437

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

12438

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

12439

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

12440

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

12441

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

12442

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

12443

\[ {}8 y+10 x +\left (5 y+7 x \right ) y^{\prime } = 0 \]

12444

\[ {}2 \sqrt {s t}-s+t s^{\prime } = 0 \]

12445

\[ {}t -s+t s^{\prime } = 0 \]

12446

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

12447

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

12448

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

12449

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

12450

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

12451

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

12452

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

12453

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

12454

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

12455

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

12456

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

12457

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

12458

\[ {}s^{\prime } \cos \left (t \right )+s \sin \left (t \right ) = 1 \]

12459

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

12460

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

12461

\[ {}y^{\prime }+\frac {n y}{x} = a \,x^{-n} \]

12462

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

12463

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

12464

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

12465

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

12466

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

12467

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

12468

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

12469

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

12470

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

12471

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

12472

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

12473

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

12474

\[ {}6 x y^{2}+4 x^{3}+3 \left (2 x^{2} y+y^{2}\right ) y^{\prime } = 0 \]

12475

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

12476

\[ {}\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}} = \frac {2 y y^{\prime }}{x^{3}} \]

12477

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

12478

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

12479

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

12480

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

12481

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

12482

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

12483

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

12484

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

12485

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

12486

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

12487

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

12488

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

12540

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

12541

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

12543

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

12544

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

12546

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

12547

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

12548

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

12552

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

12553

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

12575

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

12579

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

12580

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

12581

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

12582

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

12583

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

12585

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

12586

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

12590

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

12594

\[ {}{y^{\prime }}^{2}-4 y = 0 \]

12595

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

12596

\[ {}{y^{\prime }}^{2} = x^{6} \]

12597

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

12598

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

12600

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

12602

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

12603

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

12615

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

12616

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

12617

\[ {}y^{\prime } = 1-y \]

12618

\[ {}y^{\prime } = y+1 \]

12619

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

12620

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

12621

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

12622

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

12623

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

12624

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

12625

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