6.156 Problems 15501 to 15600

Table 6.311: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

15501

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

15502

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

15503

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

15504

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

15505

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

15506

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

15507

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

15508

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

15509

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

15510

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

15511

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

15512

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

15513

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

15514

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

15515

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

15516

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

15517

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

15518

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

15519

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

15520

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

15521

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

15522

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

15523

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

15524

\[ {} y^{\prime \prime } = 9 y \]

15525

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

15526

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

15527

\[ {} y^{\prime \prime }+12 y = 7 y^{\prime } \]

15528

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

15529

\[ {} y^{\prime \prime }+2 y^{\prime }+10 y = 0 \]

15530

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

15531

\[ {} 4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

15532

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

15533

\[ {} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0 \]

15534

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

15535

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

15536

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

15537

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+9 y = 0 \]

15538

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

15539

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

15540

\[ {} y^{\prime \prime \prime \prime }-a^{4} y = 0 \]

15541

\[ {} 12 y-7 y^{\prime }+y^{\prime \prime } = x \]

15542

\[ {} s^{\prime \prime }-a^{2} s = t +1 \]

15543

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

15544

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

15545

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

15546

\[ {} y^{\prime \prime }+6 y^{\prime }+5 y = {\mathrm e}^{2 x} \]

15547

\[ {} y^{\prime \prime }+9 y = 6 \,{\mathrm e}^{3 x} \]

15548

\[ {} y^{\prime \prime }-3 y^{\prime } = 2-6 x \]

15549

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

15550

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

15551

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 2 x +3 \]

15552

\[ {} y^{\prime \prime \prime \prime }-a^{4} y = 5 a^{4} {\mathrm e}^{a x} \sin \left (a x \right ) \]

15553

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

15554

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

15555

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

15556

\[ {} y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \]

15557

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

15558

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

15559

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

15560

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

15561

\[ {} [4 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+3 x \left (t \right ) = \sin \left (t \right ), x^{\prime }\left (t \right )+y \left (t \right ) = \cos \left (t \right )] \]

15562

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

15563

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

15564

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

15565

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

15566

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

15567

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

15568

\[ {} y^{\prime \prime }-4 y = {\mathrm e}^{2 x} \sin \left (2 x \right ) \]

15569

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

15570

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

15571

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

15572

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+6 y \left (t \right )] \]

15573

\[ {} [x^{\prime }\left (t \right ) = -4 x \left (t \right )-10 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )] \]

15574

\[ {} [x^{\prime }\left (t \right ) = 12 x \left (t \right )+18 y \left (t \right ), y^{\prime }\left (t \right ) = -8 x \left (t \right )-12 y \left (t \right )] \]

15575

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

15576

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

15577

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

15578

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

15579

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

15580

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

15581

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

15582

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

15583

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

15584

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

15585

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

15586

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

15587

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

15588

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

15589

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

15590

\[ {} [x^{\prime }\left (t \right ) = 0, y^{\prime }\left (t \right ) = x \left (t \right )] \]

15591

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

15592

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

15593

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

15594

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

15595

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

15596

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

15597

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

15598

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

15599

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

15600

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