5.9.29 Problems 2801 to 2900

Table 5.685: First order ode linear in derivative

#

ODE

Mathematica

Maple

6583

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

6584

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

6585

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

6586

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

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

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

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

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

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

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

6598

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

6599

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

6600

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

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

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

6608

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

6609

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

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

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

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

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

6623

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

6624

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

6625

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

6626

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

6627

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

6628

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

6629

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

6630

\[ {}y+x^{3} y+2 x^{2}+\left (x +4 y^{4} x +8 y^{3}\right ) y^{\prime } = 0 \]

6631

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

6632

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

6633

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

6634

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

6635

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

6636

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

6637

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

6638

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

6639

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

6640

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

6641

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

6642

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

6643

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

6644

\[ {}i^{\prime }-6 i = 10 \sin \left (2 t \right ) \]

6645

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

6646

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

6647

\[ {}\left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime } = 2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right ) \]

6648

\[ {}x y^{\prime }+y-x^{3} y^{6} = 0 \]

6649

\[ {}r^{\prime }+2 r \cos \left (\theta \right )+\sin \left (2 \theta \right ) = 0 \]

6650

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

6651

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

6652

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

6653

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

6654

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

6655

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

6656

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

6657

\[ {}2 x y^{5}-y+2 x y^{\prime } = 0 \]

6658

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

6659

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

6660

\[ {}L i^{\prime }+R i = E \sin \left (2 t \right ) \]

6661

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

6662

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

6663

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

6664

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

6665

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

6794

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

6842

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

6885

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

6886

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

6887

\[ {}y^{\prime }+20 y = 24 \]

6890

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

6891

\[ {}y^{\prime } = 25+y^{2} \]

6892

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

6893

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

6894

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

6895

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

6896

\[ {}p^{\prime } = p \left (1-p\right ) \]

6897

\[ {}y^{\prime }+4 x y = 8 x^{3} \]

6900

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

6901

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

6902

\[ {}x^{2} y^{\prime }+x y = 10 \sin \left (x \right ) \]

6903

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