3.20.2 Problems 101 to 200

Table 3.731: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

286

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

287

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

288

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

289

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

290

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

291

\[ {}y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y = 0 \]

292

\[ {}6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y = 0 \]

293

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

294

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

295

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

296

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

297

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

298

\[ {}y^{\prime \prime \prime }+10 y^{\prime \prime }+25 y^{\prime } = 0 \]

299

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

300

\[ {}2 y^{\prime \prime \prime }-y^{\prime \prime }-5 y^{\prime }-2 y = 0 \]

301

\[ {}y^{\prime \prime \prime }+27 y = 0 \]

302

\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-6 y = 0 \]

303

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y = 0 \]

304

\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y = 0 \]

305

\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+100 y^{\prime }-500 y = 0 \]

306

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

307

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

599

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

600

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

601

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

602

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

603

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

604

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

605

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

606

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

607

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

608

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

609

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

610

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

611

\[ {}y^{\prime \prime }+5 y^{\prime }+3 y = 0 \]

612

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

613

\[ {}y^{\prime \prime }+8 y^{\prime }-9 y = 0 \]

614

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

615

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

616

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

617

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

618

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

619

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

620

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

621

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

622

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

623

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

624

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

625

\[ {}y^{\prime \prime }+2 y^{\prime }-8 y = 0 \]

626

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

627

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

628

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

629

\[ {}y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4} = 0 \]

630

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

631

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

632

\[ {}y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4} = 0 \]

633

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

634

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

635

\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]

636

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

637

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

638

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

639

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

640

\[ {}5 u^{\prime \prime }+2 u^{\prime }+7 u = 0 \]

641

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

642

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

653

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

654

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

655

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

656

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

657

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

658

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

659

\[ {}4 y^{\prime \prime }+17 y^{\prime }+4 y = 0 \]

660

\[ {}16 y^{\prime \prime }+24 y^{\prime }+9 y = 0 \]

661

\[ {}25 y^{\prime \prime }-20 y^{\prime }+4 y = 0 \]

662

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

663

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

664

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

665

\[ {}9 y^{\prime \prime }+6 y^{\prime }+82 y = 0 \]

666

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

667

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

668

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

683

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

684

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

685

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

686

\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}} \]

687

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

688

\[ {}y^{\prime \prime }+9 y = 9 \sec \left (3 t \right )^{2} \]

689

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

690

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

691

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

692

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

693

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = g \left (t \right ) \]

694

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

705

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

706

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+2 u = 0 \]

707

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (\frac {t}{4}\right ) \]

708

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (2 t \right ) \]

709

\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (6 t \right ) \]

812

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