5.12.11 Problems 1001 to 1100

Table 5.839: Third and higher order linear ODE

#

ODE

Mathematica

Maple

16392

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

16393

\[ {}24 y^{\prime \prime \prime }-26 y^{\prime \prime }+9 y^{\prime }-y = 0 \]

16394

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

16395

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

16396

\[ {}8 y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+66 y^{\prime \prime \prime }-41 y^{\prime \prime }-37 y^{\prime } = 0 \]

16397

\[ {}2 y^{\left (5\right )}+7 y^{\prime \prime \prime \prime }+17 y^{\prime \prime \prime }+17 y^{\prime \prime }+5 y^{\prime } = 0 \]

16398

\[ {}y^{\left (5\right )}+8 y^{\prime \prime \prime \prime } = 0 \]

16399

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

16400

\[ {}y^{\prime \prime \prime }+9 y^{\prime \prime }+16 y^{\prime }-26 y = 0 \]

16401

\[ {}y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+60 y^{\prime \prime }+124 y^{\prime }+75 y = 0 \]

16402

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

16403

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+30 y^{\prime \prime }-56 y^{\prime }+49 y = 0 \]

16404

\[ {}\frac {31 y^{\prime \prime \prime }}{100}+\frac {56 y^{\prime \prime }}{5}-\frac {49 y^{\prime }}{5}+\frac {53 y}{10} = 0 \]

16406

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

16407

\[ {}y^{\prime \prime \prime \prime }-16 y = 1 \]

16408

\[ {}y^{\left (5\right )}-y^{\prime \prime \prime \prime } = 1 \]

16409

\[ {}y^{\prime \prime \prime \prime }+9 y^{\prime \prime } = 1 \]

16410

\[ {}y^{\prime \prime \prime \prime }+9 y^{\prime \prime } = 9 \,{\mathrm e}^{3 t} \]

16411

\[ {}y^{\prime \prime \prime }+10 y^{\prime \prime }+34 y^{\prime }+40 y = t \,{\mathrm e}^{-4 t}+2 \,{\mathrm e}^{-3 t} \cos \left (t \right ) \]

16412

\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \,{\mathrm e}^{-3 t}-t \,{\mathrm e}^{-t} \]

16413

\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-24 y^{\prime }+36 y = 108 t \]

16414

\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }-14 y^{\prime }-104 y = -111 \,{\mathrm e}^{t} \]

16415

\[ {}y^{\prime \prime \prime \prime }-10 y^{\prime \prime \prime }+38 y^{\prime \prime }-64 y^{\prime }+40 y = 153 \,{\mathrm e}^{-t} \]

16416

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

16417

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

16418

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

16419

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

16420

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

16421

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

16422

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

16423

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

16424

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

16425

\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }-11 y^{\prime }+30 y = {\mathrm e}^{4 t} \]

16426

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-10 y^{\prime }-24 y = {\mathrm e}^{-3 t} \]

16427

\[ {}y^{\prime \prime \prime }-13 y^{\prime }+12 y = \cos \left (t \right ) \]

16428

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

16429

\[ {}y^{\left (6\right )}+y^{\prime \prime \prime \prime } = -24 \]

16430

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

16431

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

16432

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

16433

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

16434

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

16435

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

16436

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

16437

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

16438

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

16439

\[ {}t y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime } = \frac {45}{8 t^{{7}/{2}}} \]

16452

\[ {}x^{3} y^{\prime \prime \prime }+22 x^{2} y^{\prime \prime }+124 x y^{\prime }+140 y = 0 \]

16453

\[ {}x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }-46 x y^{\prime }+100 y = 0 \]

16454

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

16455

\[ {}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \]

16456

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

16457

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

16458

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y = 0 \]

16459

\[ {}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+7 x y^{\prime \prime }+y^{\prime } = 0 \]

16468

\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-11 x y^{\prime }+16 y = \frac {1}{x^{3}} \]

16469

\[ {}x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+70 x y^{\prime }+80 y = \frac {1}{x^{13}} \]

16474

\[ {}x^{3} y^{\prime \prime \prime }+10 x^{2} y^{\prime \prime }-20 x y^{\prime }+20 y = 0 \]

16475

\[ {}x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 x y^{\prime }+42 y = 0 \]

16476

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

16477

\[ {}x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+17 x y^{\prime }-17 y = 0 \]

16485

\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 x y^{\prime } = 0 \]

16486

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

16487

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

16488

\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 x y^{\prime } = -8 \]

16500

\[ {}x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 x y^{\prime }+125 y = 0 \]

16501

\[ {}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 x y^{\prime }+48 y = 0 \]

16502

\[ {}x^{4} y^{\prime \prime \prime \prime }+14 x^{3} y^{\prime \prime \prime }+55 x^{2} y^{\prime \prime }+65 x y^{\prime }+15 y = 0 \]

16503

\[ {}x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+35 x y^{\prime }+45 y = 0 \]

16504

\[ {}x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 x y^{\prime }+4 y = 0 \]

16505

\[ {}x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 x y^{\prime }+58 y = 0 \]

16572

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

16573

\[ {}9 y^{\prime \prime \prime }+36 y^{\prime \prime }+40 y^{\prime } = 0 \]

16574

\[ {}9 y^{\prime \prime \prime }+12 y^{\prime \prime }+13 y^{\prime } = 0 \]

16585

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }+5 y = {\mathrm e}^{t} \]

16586

\[ {}y^{\prime \prime \prime }-12 y^{\prime }-16 y = {\mathrm e}^{4 t}-{\mathrm e}^{-2 t} \]

16587

\[ {}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+18 y^{\prime \prime }+30 y^{\prime }+25 y = {\mathrm e}^{-t} \cos \left (2 t \right )+{\mathrm e}^{-2 t} \sin \left (t \right ) \]

16588

\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }+20 y^{\prime }+25 y = t^{2} \]

16907

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

16915

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

16916

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

16928

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

16954

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

16957

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

16959

\[ {}y^{\left (6\right )}+2 y^{\left (5\right )}+y^{\prime \prime \prime \prime } = 0 \]

16961

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

16962

\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+10 y^{\prime \prime }+12 y^{\prime }+5 y = 0 \]

16965

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

16966

\[ {}y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-6 y^{\prime }-4 y = 0 \]

16967

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

16968

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

16969

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

16970

\[ {}y^{\left (5\right )} = 0 \]

16971

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

16972

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

16973

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

16990

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

16991

\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 1 \]

16992

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

16993

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