6.156 Problems 15501 to 15600

Table 6.311: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

15501

\[ {} 3 y^{\prime \prime }+8 y^{\prime }-3 y = 123 x \sin \left (3 x \right ) \]

15502

\[ {} y^{\prime \prime \prime }+8 y = {\mathrm e}^{-2 x} \]

15503

\[ {} y^{\left (6\right )}-64 y = {\mathrm e}^{-2 x} \]

15504

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

15505

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

15506

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

15507

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

15508

\[ {} y^{\prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \]

15509

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

15510

\[ {} y^{\prime \prime }+4 y = 20 \,{\mathrm e}^{4 t} \]

15511

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

15512

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

15513

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{4 t} \]

15514

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = t^{2} {\mathrm e}^{4 t} \]

15515

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 7 \]

15516

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right ) \]

15517

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right ) \]

15518

\[ {} y^{\prime \prime \prime }-27 y = {\mathrm e}^{-3 t} \]

15519

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

15520

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

15521

\[ {} y^{\prime \prime }+9 y = 27 t^{3} \]

15522

\[ {} y^{\prime \prime }+8 y^{\prime }+7 y = 165 \,{\mathrm e}^{4 t} \]

15523

\[ {} y^{\prime \prime }-8 y^{\prime }+17 y = 0 \]

15524

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t} t^{2} \]

15525

\[ {} y^{\prime \prime }+6 y^{\prime }+13 y = 0 \]

15526

\[ {} y^{\prime \prime }+8 y^{\prime }+17 y = 0 \]

15527

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

15528

\[ {} y^{\prime \prime }-4 y^{\prime }+40 y = 122 \,{\mathrm e}^{-3 t} \]

15529

\[ {} y^{\prime \prime }-9 y = 24 \,{\mathrm e}^{-3 t} \]

15530

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = {\mathrm e}^{2 t} \sin \left (3 t \right ) \]

15531

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

15532

\[ {} y^{\prime \prime }+4 y = t \]

15533

\[ {} y^{\prime \prime }+4 y = {\mathrm e}^{3 t} \]

15534

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

15535

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

15536

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 1 \]

15537

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

15538

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t} \]

15539

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \]

15540

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{t} \]

15541

\[ {} y^{\prime } = \operatorname {Heaviside}\left (t -3\right ) \]

15542

\[ {} y^{\prime } = \operatorname {Heaviside}\left (t -3\right ) \]

15543

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

15544

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

15545

\[ {} y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right ) \]

15546

\[ {} y^{\prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \]

15547

\[ {} y^{\prime \prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \]

15548

\[ {} y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \]

15549

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

15550

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

15551

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

15552

\[ {} y^{\prime \prime } = \delta \left (t -1\right )-\delta \left (t -4\right ) \]

15553

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

15554

\[ {} y^{\prime \prime }+y = \delta \left (t \right )+\delta \left (t -\pi \right ) \]

15555

\[ {} y^{\prime \prime }+y = -2 \delta \left (t -\frac {\pi }{2}\right ) \]

15556

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

15557

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

15558

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

15559

\[ {} y^{\prime \prime }+16 y = \delta \left (t -2\right ) \]

15560

\[ {} y^{\prime \prime }-16 y = \delta \left (t -10\right ) \]

15561

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

15562

\[ {} y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right ) \]

15563

\[ {} y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right ) \]

15564

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (t -4\right ) \]

15565

\[ {} y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right ) \]

15566

\[ {} y^{\prime \prime \prime }+9 y^{\prime } = \delta \left (t -1\right ) \]

15567

\[ {} y^{\prime \prime \prime \prime }-16 y = \delta \left (t \right ) \]

15568

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

15569

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

15570

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

15571

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

15572

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

15573

\[ {} y^{\prime }+\frac {y}{x -1} = 0 \]

15574

\[ {} y^{\prime }+\frac {y}{x -1} = 0 \]

15575

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

15576

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

15577

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

15578

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

15579

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

15580

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

15581

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

15582

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

15583

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

15584

\[ {} \left (-x^{2}+4\right ) y^{\prime \prime }-5 x y^{\prime }-3 y = 0 \]

15585

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

15586

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

15587

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

15588

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

15589

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

15590

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

15591

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

15592

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

15593

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

15594

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

15595

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

15596

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

15597

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

15598

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

15599

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

15600

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