4.2.49 Problems 4801 to 4900

Table 4.303: Second order linear ODE

#

ODE

Mathematica

Maple

Sympy

16235

\[ {} y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right ) \]

16236

\[ {} y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \]

16237

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

16238

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

16239

\[ {} y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right ) \]

16240

\[ {} y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right ) \]

16241

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

16242

\[ {} y^{\prime \prime }+9 y = 5 \sin \left (2 t \right ) \]

16243

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

16244

\[ {} y^{\prime \prime }+4 y = 3 \cos \left (2 t \right ) \]

16245

\[ {} y^{\prime \prime }+9 y = 2 \cos \left (3 t \right ) \]

16246

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

16247

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

16248

\[ {} y^{\prime \prime }-4 y^{\prime }+5 y = 2 \,{\mathrm e}^{t} \]

16249

\[ {} y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (t -4\right ) \]

16250

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

16251

\[ {} y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right ) \]

16252

\[ {} y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right ) \]

16253

\[ {} y^{\prime \prime }+3 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \]

16254

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

16255

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

16256

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

16257

\[ {} y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (t -1\right )-3 \delta \left (t -4\right ) \]

16258

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

16259

\[ {} y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right ) \]

16260

\[ {} y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right ) \]

16261

\[ {} y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right ) \]

16262

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

16263

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

16264

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

16265

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

16271

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

16272

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

16274

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

16275

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

16285

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

16286

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

16294

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

16496

\[ {} x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

16497

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

16498

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

16499

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

16500

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

16501

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

16508

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

16510

\[ {} y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x} \]

16518

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

16524

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

16528

\[ {} y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x} \]

16530

\[ {} x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \]

16531

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

16532

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

16533

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

16536

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

16549

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

16550

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

16551

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

16556

\[ {} y^{\prime \prime } = 2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x} \]

16559

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

16560

\[ {} y^{\prime \prime }-10 y^{\prime }+25 y = 0 \]

16561

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

16562

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

16563

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

16564

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

16565

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

16566

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

16567

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

16568

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

16569

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

16570

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

16571

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

16572

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \]

16573

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = 9 \,{\mathrm e}^{2 x} \]

16574

\[ {} y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{4 x} \]

16575

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

16576

\[ {} x^{2} y^{\prime \prime }-20 y = 27 x^{5} \]

16577

\[ {} x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x} \]

16578

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

16583

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

16584

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

16585

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

16586

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

16587

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

16588

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

16589

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

16590

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

16591

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

16592

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

16593

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

16596

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

16597

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

16598

\[ {} y^{\prime \prime }-10 y^{\prime }+9 y = 0 \]

16599

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

16602

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

16603

\[ {} y^{\prime \prime }+2 y^{\prime }-24 y = 0 \]

16604

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

16605

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

16606

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

16607

\[ {} 3 y^{\prime \prime }+7 y^{\prime }-6 y = 0 \]

16608

\[ {} y^{\prime \prime }-8 y^{\prime }+15 y = 0 \]