4.20.37 Problems 3601 to 3700

Table 4.975: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

18311

\[ {} y^{\left (6\right )}-y = x^{10} \]

18312

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

18313

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

18314

\[ {} y^{\prime \prime \prime }-y^{\prime \prime } = 12 x -2 \]

18315

\[ {} y^{\prime \prime \prime }+y^{\prime \prime } = 9 x^{2}-2 x +1 \]

18316

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

18317

\[ {} y^{\prime \prime }-7 y^{\prime }+12 y = {\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right ) \]

18318

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

18319

\[ {} y^{\prime \prime \prime }-8 y = 16 x^{2} \]

18320

\[ {} y^{\prime \prime \prime \prime }-y = -x^{3}+1 \]

18321

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

18322

\[ {} y^{\prime \prime \prime \prime } = \frac {1}{x^{3}} \]

18323

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

18324

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

18325

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = {\mathrm e}^{2 x} \]

18326

\[ {} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 12 \,{\mathrm e}^{-x} \]

18327

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

18374

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

18375

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

18376

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

18377

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

18378

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

18382

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

18383

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 t} \]

18384

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

18385

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

18386

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

18438

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

18439

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

18440

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

18441

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

18442

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

18443

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

18444

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

18445

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

18446

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

18447

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

18448

\[ {} x^{\prime \prime }+2 x^{\prime }+4 x = {\mathrm e}^{t} \cos \left (2 t \right ) \]

18449

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

18450

\[ {} x^{\prime \prime }+4 x^{\prime }+3 x = t \sin \left (t \right ) \]

18451

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

18486

\[ {} \theta ^{\prime \prime } = -p^{2} \theta \]

18501

\[ {} \theta ^{\prime \prime }-p^{2} \theta = 0 \]

18502

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

18503

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

18504

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

18505

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

18506

\[ {} v^{\prime \prime }-6 v^{\prime }+13 v = {\mathrm e}^{-2 u} \]

18507

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

18508

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

18510

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

18513

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

18514

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

18515

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

18520

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

18528

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

18576

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

18577

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

18578

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

18579

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

18580

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

18581

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

18582

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

18583

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

18584

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

18585

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

18586

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

18587

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

18588

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

18589

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

18590

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

18591

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

18592

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

18593

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

18594

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

18595

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

18596

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

18597

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

18598

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

18599

\[ {} e y^{\prime \prime } = \frac {P \left (\frac {L}{2}-x \right )}{2} \]

18600

\[ {} e y^{\prime \prime } = \frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2} \]

18601

\[ {} e y^{\prime \prime } = -\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2} \]

18602

\[ {} e y^{\prime \prime } = -P \left (L -x \right ) \]

18603

\[ {} e y^{\prime \prime } = -P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2} \]

18604

\[ {} e y^{\prime \prime } = P \left (-y+a \right ) \]

18619

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

18621

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

18627

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

18647

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

18788

\[ {} y^{\prime \prime }+3 y^{\prime }-54 y = 0 \]

18789

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

18790

\[ {} 2 y^{\prime \prime }+5 y^{\prime }-12 y = 0 \]

18791

\[ {} 9 y^{\prime \prime }+18 y^{\prime }-16 y = 0 \]

18792

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

18793

\[ {} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0 \]

18794

\[ {} y^{\prime \prime }+8 y^{\prime }+25 y = 0 \]

18795

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

18796

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

18797

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x} \]

18798

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