6.226 Problems 22501 to 22600

Table 6.451: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

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

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

22555

\[ {} i^{\prime } = \frac {t -i t}{t^{2}+1} \]

22556

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

22557

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

22558

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

22559

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

22560

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

22561

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

22562

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

22563

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

22564

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

22565

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

22566

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

22567

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

22568

\[ {} i^{\prime }+3 i = {\mathrm e}^{-2 t} \]

22569

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

22570

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

22571

\[ {} r^{\prime } = t -\frac {r}{3 t} \]

22572

\[ {} i^{\prime }+2 i = 10 \,{\mathrm e}^{-2 t} \]

22573

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

22574

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

22575

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

22576

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

22577

\[ {} x y^{\prime }+3 = 4 x \,{\mathrm e}^{-y} \]

22578

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

22579

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

22580

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

22581

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

22582

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

22583

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

22584

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

22585

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

22586

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

22587

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

22588

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

22589

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

22590

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

22591

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

22592

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

22593

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

22594

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

22595

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

22596

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

22597

\[ {} i^{\prime \prime } = t^{2}+1 \]

22598

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

22599

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

22600

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