6.76 Problems 7501 to 7600

Table 6.151: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

7501

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

7502

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

7503

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

7504

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

7505

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

7506

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

7507

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

7508

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

7509

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

7510

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

7511

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

7512

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

7513

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

7514

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

7515

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

7516

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

7517

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

7518

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

7519

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

7520

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

7521

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

7522

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

7523

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

7524

\[ {} x^{\prime }+t x^{3}+\frac {x}{t} = 0 \]

7525

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

7526

\[ {} r^{\prime } = r^{2}+\frac {2 r}{t} \]

7527

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

7528

\[ {} x +y-1+\left (y-x -5\right ) y^{\prime } = 0 \]

7529

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

7530

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

7531

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

7532

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

7533

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

7534

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

7535

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

7536

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

7537

\[ {} y^{\prime }-4 y = 32 x^{2} \]

7538

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

7539

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

7540

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

7541

\[ {} t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}} = 0 \]

7542

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

7543

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

7544

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

7545

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

7546

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

7547

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

7548

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

7549

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

7550

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

7551

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

7552

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

7553

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

7554

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

7555

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

7556

\[ {} 2 x -2 y-8+\left (x -3 y-6\right ) y^{\prime } = 0 \]

7557

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

7558

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

7559

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

7560

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

7561

\[ {} 3 x -y-5+\left (x -y+1\right ) y^{\prime } = 0 \]

7562

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

7563

\[ {} 4 x y^{3}-9 y^{2}+4 x y^{2}+\left (3 x^{2} y^{2}-6 x y+2 x^{2} y\right ) y^{\prime } = 0 \]

7564

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

7565

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

7566

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

7567

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

7568

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

7569

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

7570

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

7571

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

7572

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

7573

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

7574

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

7575

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

7576

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

7577

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

7578

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

7579

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

7580

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

7581

\[ {} m y^{\prime \prime }+k y = 0 \]

7582

\[ {} m y^{\prime \prime }+b y^{\prime }+k y = 0 \]

7583

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

7584

\[ {} 2 y^{\prime \prime }+18 y = 0 \]

7585

\[ {} y^{\prime \prime }+6 y^{\prime }+12 y = 0 \]

7586

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

7587

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

7588

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = -50 \sin \left (5 t \right ) \]

7589

\[ {} y^{\prime \prime }+2 y^{\prime }+4 y = 6 \cos \left (2 t \right )+8 \sin \left (2 t \right ) \]

7590

\[ {} m y^{\prime \prime }+b y^{\prime }+k y = \cos \left (\omega t \right ) \]

7591

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{10}+25 y = \cos \left (\omega t \right ) \]

7592

\[ {} y^{\prime \prime }+25 y = \cos \left (\omega t \right ) \]

7593

\[ {} 2 y^{\prime \prime }+7 y^{\prime }-4 y = 0 \]

7594

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

7595

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]

7596

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

7597

\[ {} y^{\prime \prime }+8 y^{\prime }+16 y = 0 \]

7598

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

7599

\[ {} 6 y^{\prime \prime }+y^{\prime }-2 y = 0 \]

7600

\[ {} z^{\prime \prime }+z^{\prime }-z = 0 \]