4.9.80 Problems 7901 to 8000

Table 4.997: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

22448

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

22449

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

22455

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

22456

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

22457

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

22458

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

22459

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

22460

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

22461

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

22462

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

22463

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

22464

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

22465

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

22466

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

22467

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

22468

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

22469

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

22470

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

22471

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

22474

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

22475

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

22476

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

22477

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

22478

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

22479

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

22480

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

22481

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

22482

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

22483

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

22484

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

22485

\[ {} i^{\prime }+5 i = 10 \]

22486

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

22487

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

22488

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

22489

\[ {} r^{\prime } = \frac {\sin \left (t \right )+{\mathrm e}^{r} \sin \left (t \right )}{3 \,{\mathrm e}^{r}+{\mathrm e}^{r} \cos \left (2 t \right )} \]

22490

\[ {} r^{\prime } = \frac {\sin \left (t \right )+{\mathrm e}^{r} \sin \left (t \right )}{3 \,{\mathrm e}^{r}+{\mathrm e}^{r} \cos \left (2 t \right )} \]

22491

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

22492

\[ {} U^{\prime } = \frac {U+1}{\sqrt {s}+\sqrt {s U}} \]

22493

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

22494

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

22495

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

22496

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

22497

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

22498

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

22499

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

22500

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

22501

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

22502

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

22503

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

22504

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

22505

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

22506

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

22507

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

22508

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

22509

\[ {} y^{\prime } = \frac {6 x^{2}-5 x y-2 y^{2}}{6 x^{2}-8 x y+y^{2}} \]

22510

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

22511

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

22512

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

22513

\[ {} \left (3 x -y-9\right ) y^{\prime } = 10-2 x +2 y \]

22514

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

22515

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

22516

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

22517

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

22518

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

22519

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

22520

\[ {} y^{\prime } = \frac {3 x^{5}+3 x^{2} y^{2}}{2 x^{3} y-2 y^{3}} \]

22521

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

22522

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

22523

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

22524

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

22525

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

22526

\[ {} 3 x +4 y y^{\prime } = 0 \]

22527

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

22528

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

22529

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

22530

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

22531

\[ {} r^{\prime } = \frac {r \sin \left (t \right )}{2 r \cos \left (t \right )-1} \]

22532

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

22533

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

22534

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

22535

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

22536

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

22537

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

22538

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

22539

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

22540

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

22541

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

22542

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

22543

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

22544

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

22545

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

22546

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

22547

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

22548

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

22549

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

22550

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

22551

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

22552

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

22553

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

22554

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