2.7 Problems 601 to 700

Table 2.7: Main lookup table

#

ODE

Mathematica result

Maple result

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

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

643

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

644

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

645

\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+\frac {5 y}{4} = 0 \]

646

\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 0 \]

647

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

648

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

649

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

650

\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }+10 y = 0 \]

651

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

652

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

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

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

669

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

670

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

671

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

672

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

673

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

674

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

675

\[ {}x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0 \]

676

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

677

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

678

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

679

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

680

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

681

\[ {}4 t^{2} y^{\prime \prime }-8 t y^{\prime }+9 y = 0 \]

682

\[ {}t^{2} y^{\prime \prime }+5 t y^{\prime }+13 y = 0 \]

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

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

688

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

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

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

694

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

695

\[ {}t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1 \]

696

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

697

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

698

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

699

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{2} \ln \relax (x ) \]

700

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