3.4.2 Problems 101 to 200

Table 3.339: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

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

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

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

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

705

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

706

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

833

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

834

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

835

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

836

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

837

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

1087

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

1088

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

1089

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

1090

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

1091

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

1092

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

1093

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

1094

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

1095

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

1096

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

1097

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

1098

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

1099

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

1100

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

1101

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

1102

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

1103

\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }+\left (6 x -8\right ) y = 0 \]

1104

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

1105

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

1106

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

1124

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

1125

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

1126

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

1127

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

1128

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

1129

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

1130

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

1131

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

1132

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

1133

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0 \]

1134

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

1135

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

1136

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

1138

\[ {}\left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = 0 \]

1712

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

1713

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

1714

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

1715

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

1716

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

1717

\[ {}6 y^{\prime \prime }-7 y^{\prime }+y = 0 \]

1718

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

1719

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

1720

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

1721

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

1722

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

1723

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

1724

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