6.166 Problems 16501 to 16600

Table 6.331: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

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

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

16524

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

16525

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

16526

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

16527

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

16528

\[ {} x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y = 0 \]

16529

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

16530

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

16531

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

16532

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

16533

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+25 y = 0 \]

16534

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 8 x \]

16535

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

16536

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

16537

\[ {} \left (2 x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-3 y = 0 \]

16538

\[ {} 3 x y^{\prime \prime }+11 y^{\prime }-y = 0 \]

16539

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

16540

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

16541

\[ {} x \left (1-x \right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y = 0 \]

16542

\[ {} x \left (1+x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }-10 y = 0 \]

16543

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

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

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

16569

\[ {} [x^{\prime }\left (t \right ) = 6, y^{\prime }\left (t \right ) = \cos \left (t \right )] \]

16570

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 1] \]

16571

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

16572

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

16573

\[ {} [x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 1] \]

16574

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

16575

\[ {} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+6 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )] \]

16576

\[ {} [x^{\prime }\left (t \right ) = 8 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+6 y \left (t \right )] \]

16577

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

16578

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

16579

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

16580

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

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

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

16585

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

16586

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

16587

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

16588

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

16589

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

16590

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

16591

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

16592

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

16593

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

16594

\[ {} y^{\prime } = \left (3 x -y\right )^{{1}/{3}}-1 \]

16595

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

16596

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

16597

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

16598

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

16599

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

16600

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