3.8.8 Problems 701 to 800

Table 3.499: Third and higher order ode

#

ODE

Mathematica

Maple

11873

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

12044

\[ {}x^{\prime \prime \prime }-6 x^{\prime \prime }+11 x^{\prime }-6 x = {\mathrm e}^{-t} \]

12045

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

12046

\[ {}x^{\prime \prime \prime \prime }-4 x^{\prime \prime \prime }+8 x^{\prime \prime }-8 x^{\prime }+4 x = \sin \left (t \right ) \]

12047

\[ {}x^{\prime \prime \prime \prime }-5 x^{\prime \prime }+4 x = {\mathrm e}^{t} \]

12166

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

12174

\[ {}y^{\prime \prime \prime \prime }-16 y = x^{2}-{\mathrm e}^{x} \]

12175

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

12176

\[ {}x^{\left (6\right )}-x^{\prime \prime \prime \prime } = 1 \]

12177

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

12188

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

12193

\[ {}y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime } = x \]

12194

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

12197

\[ {}x^{\prime \prime \prime \prime }+x = t^{3} \]

12201

\[ {}y^{\left (6\right )}-y = {\mathrm e}^{2 x} \]

12202

\[ {}y^{\left (6\right )}+2 y^{\prime \prime \prime \prime }+y^{\prime \prime } = x +{\mathrm e}^{x} \]

12203

\[ {}6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0 \]

12223

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

12225

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

12226

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

12227

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

12229

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

12235

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

12238

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

12240

\[ {}\sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime } = 1 \]

12243

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

12245

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

12247

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

12294

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

12302

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

12303

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

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

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

12499

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

12500

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

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

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

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

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

13490

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

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

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

13535

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

13556

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