3.12.8 Problems 701 to 800

Table 3.671: Third and higher order linear ODE

#

ODE

Mathematica

Maple

12304

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

12305

\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }+29 y^{\prime } = 0 \]

12306

\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime } = 0 \]

12307

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime } = 0 \]

12308

\[ {}y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y = 0 \]

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

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

12359

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

12361

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

12422

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

12489

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

12491

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

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

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

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

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

12589

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

12608

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \]

12745

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

12755

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

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

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

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

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

12779

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = \left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right ) \]

12780

\[ {}y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y = {\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right ) \]

12781

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \]

12782

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

12783

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

12784

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

12791

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

12798

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

12806

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

13264

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

13488

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

13489

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

13491

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

13511

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

13512

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

13531

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

13534

\[ {}y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }-83 y-25 = 0 \]

13556

\[ {}y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y = 0 \]

13557

\[ {}y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y = {\mathrm e}^{3 x} \sin \left (x \right ) \]

13558

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+16 y = 0 \]

13559

\[ {}x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y = 0 \]

13571

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

13572

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

13577

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

13578

\[ {}y^{\prime \prime \prime \prime }-10 y^{\prime \prime }+9 y = 0 \]

13617

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

13618

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

13619

\[ {}y^{\prime \prime \prime \prime }-34 y^{\prime \prime }+225 y = 0 \]

13620

\[ {}y^{\prime \prime \prime \prime }-81 y = 0 \]

13621

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

13622

\[ {}y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = 0 \]

13623

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

13624

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

13625

\[ {}y^{\prime \prime \prime }-8 y^{\prime \prime }+37 y^{\prime }-50 y = 0 \]

13626

\[ {}y^{\prime \prime \prime }-9 y^{\prime \prime }+31 y^{\prime }-39 y = 0 \]

13627

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

13628

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+10 y^{\prime \prime }+18 y^{\prime }+9 y = 0 \]

13629

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

13630

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

13631

\[ {}y^{\prime \prime \prime \prime }+26 y^{\prime \prime }+25 y = 0 \]

13632

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

13633

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

13634

\[ {}y^{\prime \prime \prime }+216 y = 0 \]

13635

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

13636

\[ {}y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y = 0 \]

13637

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

13638

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

13639

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

13640

\[ {}4 y^{\prime \prime \prime \prime }+15 y^{\prime \prime }-4 y = 0 \]

13641

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+16 y^{\prime }-16 y = 0 \]

13642

\[ {}y^{\left (6\right )}+16 y^{\prime \prime \prime }+64 y = 0 \]

13667

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

13668

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