4.2.60 Problems 5901 to 6000

Table 4.325: Second order linear ODE

#

ODE

Mathematica

Maple

Sympy

19072

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

19073

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

19076

\[ {} \frac {7 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right ) \]

19077

\[ {} \frac {8 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right ) \]

19179

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

19281

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

19282

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

19283

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

19287

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

19288

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

19291

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

19292

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

19293

\[ {} y^{\prime \prime }+p_{1} y^{\prime }+p_{2} y = 0 \]

19294

\[ {} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0 \]

19295

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

19300

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

19302

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

19303

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

19306

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

19307

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

19308

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

19309

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

19310

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

19311

\[ {} y^{\prime \prime }+9 y = \ln \left (2 \sin \left (\frac {x}{2}\right )\right ) \]

19312

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

19313

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

19314

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

19315

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

19317

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

19318

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

19319

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

19320

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

19321

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

19322

\[ {} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y = -3 \,{\mathrm e}^{x^{2}} \sin \left (2 x \right ) \]

19323

\[ {} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}} = 0 \]

19346

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

19347

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

19387

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

19475

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

19479

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

19500

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

19507

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

19535

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

19536

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

19537

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

19538

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

19539

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

19540

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

19541

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

19542

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

19543

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

19544

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

19545

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

19546

\[ {} -5 y-3 x y^{\prime }+x^{2} y^{\prime \prime } = 0 \]

19547

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

19548

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

19549

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

19550

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

19551

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

19552

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

19553

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

19554

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

19555

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

19557

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

19558

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

19559

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

19560

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

19561

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

19562

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

19563

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

19564

\[ {} y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1} = 0 \]

19565

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

19566

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

19567

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

19568

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

19569

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

19570

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

19571

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

19572

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

19573

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

19574

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

19575

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

19576

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

19577

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

19578

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

19579

\[ {} 20 y-9 y^{\prime }+y^{\prime \prime } = 0 \]

19580

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

19581

\[ {} 4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

19582

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

19583

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]

19584

\[ {} 4 y^{\prime \prime }+20 y^{\prime }+25 y = 0 \]

19585

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

19586

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

19587

\[ {} 4 y^{\prime \prime }-8 y^{\prime }+7 y = 0 \]

19588

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

19589

\[ {} 16 y^{\prime \prime }-8 y^{\prime }+y = 0 \]

19590

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

19591

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

19592

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

19593

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