4.3.61 Problems 6001 to 6100

Table 4.405: Second order ode

#

ODE

Mathematica

Maple

Sympy

18307

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

18309

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

18312

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

18313

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

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

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

18327

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

18335

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

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

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

18379

\[ {} x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (4 x +9\right ) y = 0 \]

18380

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

18381

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

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

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

18408

\[ {} x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0 \]

18434

\[ {} t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x = 0 \]

18437

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

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

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

18452

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

18454

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

18455

\[ {} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y^{\prime \prime }+n y \sin \left (x \right ) = 0 \]

18457

\[ {} v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \]

18459

\[ {} \sqrt {y^{\prime }+y} = \left (y^{\prime \prime }+2 x \right )^{{1}/{4}} \]

18486

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

18488

\[ {} y^{\prime \prime } = \frac {m \sqrt {1+{y^{\prime }}^{2}}}{k} \]

18489

\[ {} \phi ^{\prime \prime } = \frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}} \]

18501

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

18502

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

18503

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

18504

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

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

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

18516

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

18517

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

18518

\[ {} y^{\prime \prime } = c \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \]

18520

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

18521

\[ {} 1+{y^{\prime }}^{2}+\frac {m y^{\prime \prime }}{\sqrt {1+{y^{\prime }}^{2}}} = 0 \]

18523

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

18527

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = \frac {1}{x} \]

18528

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

18529

\[ {} v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0 \]

18530

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

18531

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

18532

\[ {} \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = r y^{\prime \prime } \]

18534

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

18536

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

18537

\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 0 \]

18539

\[ {} v^{\prime \prime }+\frac {2 x v^{\prime }}{x^{2}+1}+\frac {v}{\left (x^{2}+1\right )^{2}} = 0 \]

18576

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

18577

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

18585

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

18587

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

18588

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

18591

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

18592

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

18593

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

18595

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

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

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

18606

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

18610

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

18611

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

18612

\[ {} \left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 2 x \]

18613

\[ {} \left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = x \]

18614

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

18615

\[ {} \left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y = 0 \]

18616

\[ {} \left (3 x^{2}+x \right ) y^{\prime \prime }+2 \left (1+6 x \right ) y^{\prime }+6 y = \sin \left (x \right ) \]

18619

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

18620

\[ {} x^{2} y^{\prime \prime } = \ln \left (x \right ) \]

18621

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

18622

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

18623

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

18624

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

18625

\[ {} \left (x^{2}+1\right ) y^{\prime \prime }-1-{y^{\prime }}^{2} = 0 \]