3.20.19 Problems 1801 to 1900

Table 3.765: Second or higher order ODE with constant coefficients




#

ODE

Mathematica

Maple





12337

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t & 0\le t <\frac {\pi }{2} \\ 8 \pi & \frac {\pi }{2}\le t \end {array}\right . \]





12338

\[ {}y^{\prime \prime }+4 \pi ^{2} y = 3 \delta \left (t -\frac {1}{3}\right )-\delta \left (-1+t \right ) \]





12339

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





12340

\[ {}y^{\prime \prime }+4 y^{\prime }+29 y = 5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right ) \]





12341

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





12342

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





12343

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \delta \left (-1+t \right ) \]





12345

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+4 y^{\prime }+4 y = 8 \]





12346

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





12347

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y = 8 \,{\mathrm e}^{2 t}-5 \,{\mathrm e}^{t} \]





12348

\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y = -t^{2}+2 t -10 \]





12349

\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 12 \operatorname {Heaviside}\left (t \right )-12 \operatorname {Heaviside}\left (-1+t \right ) \]





12350

\[ {}y^{\prime \prime \prime \prime }-16 y = 32 \operatorname {Heaviside}\left (t \right )-32 \operatorname {Heaviside}\left (t -\pi \right ) \]





12356

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





12357

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





12358

\[ {}y^{\prime \prime }-3 y^{\prime }-7 y = 4 \]





12359

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 5 \]





12360

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





12361

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





12396

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





12397

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





12399

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





12413

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





12414

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





12415

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





12423

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





12489

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





12492

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





12501

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





12502

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





12503

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





12504

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





12505

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





12506

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





12507

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





12508

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





12509

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





12510

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





12511

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





12512

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





12513

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





12514

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





12515

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





12516

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





12517

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





12518

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





12519

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





12520

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





12521

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





12522

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





12523

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





12524

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





12525

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





12526

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





12527

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





12528

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





12529

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





12530

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





12531

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





12532

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





12533

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





12534

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





12535

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





12542

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





12545

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





12577

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





12587

\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 0 \]





12588

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





12589

\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime } = 0 \]





12599

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





12601

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





12604

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





12605

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





12606

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





12607

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





12744

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





12750

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





12751

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





12754

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





12755

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





12757

\[ {}y^{\prime \prime }-4 y = 31 \]





12758

\[ {}y^{\prime \prime }+9 y = 27 x +18 \]





12760

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





12761

\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+6 y^{\prime }-4 y = 0 \]





12762

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





12763

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





12764

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y = 0 \]





12765

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





12766

\[ {}36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y = 0 \]





12767

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





12768

\[ {}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35 y^{\prime \prime }+16 y^{\prime }-52 y = 0 \]





12769

\[ {}y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y = 0 \]





12770

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





12771

\[ {}y^{\prime \prime \prime }+\left (-3-4 i\right ) y^{\prime \prime }+\left (-4+12 i\right ) y^{\prime }+12 y = 0 \]





12772

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





12774

\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x} \]





12775

\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \]





12776

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





12777

\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 6 x -20-120 \,{\mathrm e}^{x} x^{2} \]





12778

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y = 36 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \]