4.9.77 Problems 7601 to 7700

Table 4.991: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

21528

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

21529

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

21530

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

21531

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

21532

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

21533

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

21534

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

21535

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

21536

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

21537

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

21538

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

21539

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

21540

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

21541

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

21542

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

21543

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

21544

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

21545

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

21546

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

21547

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

21548

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

21549

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

21550

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

21551

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

21552

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

21553

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

21554

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

21555

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

21556

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

21557

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

21558

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

21559

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

21560

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

21561

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

21562

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

21563

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

21564

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

21565

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

21566

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

21567

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

21568

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

21569

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

21570

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

21571

\[ {} y^{\prime }-\frac {3 y}{x} = x^{4} y^{{1}/{3}} \]

21572

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

21573

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

21574

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

21577

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

21578

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

21579

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

21580

\[ {} y^{\prime } = {\mathrm e}^{2 x}+\left (2+\frac {5 \,{\mathrm e}^{x}}{2}\right ) y+y^{2} \]

21581

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

21582

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

21583

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

21625

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

21626

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

21627

\[ {} y^{\prime }-5 y = 3 \,{\mathrm e}^{x}-2 x +1 \]

21628

\[ {} y^{\prime }-5 y = x^{3} {\mathrm e}^{x}-x \,{\mathrm e}^{5 x} \]

21629

\[ {} y^{\prime }-5 y = \left (x -1\right ) \sin \left (x \right )+\left (1+x \right ) \cos \left (x \right ) \]

21654

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

21709

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

21710

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

21711

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

21712

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

21713

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

21714

\[ {} x -2 y+1+\left (4 x -3 y-6\right ) y^{\prime } = 0 \]

21719

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

21722

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

21723

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

21724

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

21726

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

21738

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

21741

\[ {} y^{\prime }-k y = A \]

21742

\[ {} L i^{\prime }+R i = E_{0} \]

21819

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

21820

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

21821

\[ {} y^{\prime }-5 y = {\mathrm e}^{5 t} \]

21822

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

21823

\[ {} -2 y+y^{\prime } = {\mathrm e}^{5 t} \]

21824

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

21825

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

21826

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

21827

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

21848

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

21872

\[ {} 2 x^{4} y y^{\prime }+y^{4} = 4 x^{6} \]

21906

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

21907

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

21910

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

21911

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

21912

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

21913

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

21914

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

21915

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

21916

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

21917

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

21918

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

21919

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

21920

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

21921

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

21922

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