4.20.31 Problems 3001 to 3100

Table 4.963: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

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

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

16479

\[ {} y^{\prime \prime }-7 y^{\prime }+10 y = 0 \]

16480

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

16481

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

16484

\[ {} y^{\prime \prime }+7 y^{\prime }+10 y = 0 \]

16485

\[ {} 6 y^{\prime \prime }+5 y^{\prime }-4 y = 0 \]

16486

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

16487

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

16488

\[ {} y^{\prime \prime }-10 y^{\prime }+34 y = 0 \]

16489

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

16490

\[ {} 15 y^{\prime \prime }-11 y^{\prime }+2 y = 0 \]

16491

\[ {} 20 y^{\prime \prime }+y^{\prime }-y = 0 \]

16492

\[ {} 12 y^{\prime \prime }+8 y^{\prime }+y = 0 \]

16493

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

16494

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

16495

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

16496

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

16497

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

16498

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

16499

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

16500

\[ {} y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}} \]

16501

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

16502

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

16503

\[ {} y^{\prime \prime }-6 y^{\prime }+13 y = 3 \,{\mathrm e}^{-2 t} \]

16504

\[ {} y^{\prime \prime }+9 y^{\prime }+20 y = -2 t \,{\mathrm e}^{t} \]

16505

\[ {} y^{\prime \prime }+7 y^{\prime }+12 y = 3 t^{2} {\mathrm e}^{-4 t} \]

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

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

16510

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

16511

\[ {} y^{\prime \prime }+10 y^{\prime }+16 y = 0 \]

16512

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

16513

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

16514

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

16515

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

16516

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

16517

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

16518

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

16519

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

16520

\[ {} y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \]

16521

\[ {} y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \]

16522

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

16523

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

16525

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

16526

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

16544

\[ {} 4 x^{\prime \prime }+9 x = 0 \]

16545

\[ {} 9 x^{\prime \prime }+4 x = 0 \]

16546

\[ {} x^{\prime \prime }+64 x = 0 \]

16547

\[ {} x^{\prime \prime }+100 x = 0 \]

16548

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

16549

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

16550

\[ {} x^{\prime \prime }+16 x = 0 \]

16551

\[ {} x^{\prime \prime }+256 x = 0 \]

16552

\[ {} x^{\prime \prime }+9 x = 0 \]

16553

\[ {} 10 x^{\prime \prime }+\frac {x}{10} = 0 \]

16554

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

16555

\[ {} \frac {x^{\prime \prime }}{32}+2 x^{\prime }+x = 0 \]

16556

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

16557

\[ {} 4 x^{\prime \prime }+2 x^{\prime }+8 x = 0 \]

16558

\[ {} x^{\prime \prime }+4 x^{\prime }+13 x = 0 \]

16559

\[ {} x^{\prime \prime }+4 x^{\prime }+20 x = 0 \]

16560

\[ {} x^{\prime \prime }+x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

16561

\[ {} x^{\prime \prime }+x = \left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

16562

\[ {} x^{\prime \prime }+x = \left \{\begin {array}{cc} t & 0\le t <1 \\ -t +2 & 1\le t <2 \\ 0 & 2\le t \end {array}\right . \]

16563

\[ {} x^{\prime \prime }+4 x^{\prime }+13 x = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 1-t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \]

16564

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

16565

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

16566

\[ {} x^{\prime \prime }+x = \cos \left (\frac {9 t}{10}\right ) \]

16567

\[ {} x^{\prime \prime }+x = \cos \left (\frac {7 t}{10}\right ) \]

16568

\[ {} x^{\prime \prime }+\frac {x^{\prime }}{10}+x = 3 \cos \left (2 t \right ) \]

16581

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

16582

\[ {} x^{\prime \prime }+6 x^{\prime }+9 x = 0 \]

16583

\[ {} x^{\prime \prime }+16 x = t \sin \left (t \right ) \]

16584

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

16827

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

16832

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

16833

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

16836

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

16837

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

16839

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

16840

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

16856

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

16873

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

16874

\[ {} 3 y^{\prime \prime }-2 y^{\prime }-8 y = 0 \]

16875

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

16876

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

16877

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

16878

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

16879

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

16880

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

16881

\[ {} 4 y^{\prime \prime }-8 y^{\prime }+5 y = 0 \]

16882

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

16883

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

16884

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

16885

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