4.19.5 Problems 401 to 500

Table 4.897: Third and higher order non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

15410

\[ {} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 32 \,{\mathrm e}^{4 x} \]

15411

\[ {} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime } = 32 x \]

15412

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

15413

\[ {} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 \cos \left (2 x \right ) \]

15414

\[ {} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 6 \,{\mathrm e}^{x} \]

15415

\[ {} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x} \]

15416

\[ {} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} \sin \left (3 x \right ) \]

15417

\[ {} y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime } = x^{2} {\mathrm e}^{3 x} \sin \left (3 x \right ) \]

15418

\[ {} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 30 x \cos \left (2 x \right ) \]

15419

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

15420

\[ {} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 3 x \,{\mathrm e}^{x} \cos \left (x \right ) \]

15421

\[ {} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 5 x^{5} {\mathrm e}^{2 x} \]

15450

\[ {} y^{\prime \prime \prime }-4 y^{\prime } = 30 \,{\mathrm e}^{3 x} \]

15451

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

15452

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

15453

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

15454

\[ {} y^{\prime \prime \prime \prime }-81 y = \sinh \left (x \right ) \]

15455

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 x y^{\prime }+9 y = 12 x \sin \left (x^{2}\right ) \]

15478

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

15502

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

15503

\[ {} y^{\left (6\right )}-64 y = {\mathrm e}^{-2 x} \]

15518

\[ {} y^{\prime \prime \prime }-27 y = {\mathrm e}^{-3 t} \]

15566

\[ {} y^{\prime \prime \prime }+9 y^{\prime } = \delta \left (t -1\right ) \]

15567

\[ {} y^{\prime \prime \prime \prime }-16 y = \delta \left (t \right ) \]

15704

\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }+5 y^{\prime }+y = {\mathrm e}^{x} \]

16327

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

16328

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

16329

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

16330

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

16331

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

16332

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

16333

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

16334

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

16335

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

16336

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

16337

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

16338

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

16339

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

16340

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

16341

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

16342

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

16343

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

16344

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

16345

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

16346

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

16347

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

16348

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

16349

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

16350

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

16351

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

16352

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

16353

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

16354

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

16355

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

16356

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

16357

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

16358

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

16359

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

16360

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

16389

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

16390

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

16409

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

16506

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

16507

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

16508

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

16509

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

16828

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

16836

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

16837

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

16911

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

16912

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

16913

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

16914

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

16915

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

16916

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

16917

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

16918

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

16919

\[ {} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime } = 1 \]

16920

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

16921

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

16922

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

16923

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

16924

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

16925

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

16926

\[ {} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y = a \sin \left (n x +\alpha \right ) \]

16927

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

16928

\[ {} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = \sin \left (x \right ) \]

16929

\[ {} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x} \]

16930

\[ {} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = x \,{\mathrm e}^{x} \]

16934

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

16935

\[ {} 5 y^{\prime \prime \prime }-7 y^{\prime \prime } = 3 \]

16936

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

16937

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

16938

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

16961

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

16962

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

16964

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

16967

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

16968

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

16969

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