5.26.21 Problems 2001 to 2100

Table 5.1159: Second order, Linear, Homogeneous and non-constant coefficients

#

ODE

Mathematica

Maple

14310

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

14312

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

14314

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

14320

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

14327

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

14328

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

14329

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

14345

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

14346

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

14347

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

14348

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

14349

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

14350

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

14488

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

14492

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

14988

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

15210

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

15213

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

15214

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

15244

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

15263

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

15264

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

15274

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

15275

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

15276

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

15277

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

15278

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

15279

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

15281

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

15282

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

15283

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

15284

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

15285

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

15300

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

15301

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

15302

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

15303

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

15304

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

15305

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

15306

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

15379

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 0 \]

15380

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

15381

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

15382

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

15383

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

15384

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \]

15385

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

15386

\[ {}x^{2} y^{\prime \prime }-19 x y^{\prime }+100 y = 0 \]

15387

\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+29 y = 0 \]

15388

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+10 y = 0 \]

15389

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+29 y = 0 \]

15390

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

15391

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

15392

\[ {}4 x^{2} y^{\prime \prime }+37 y = 0 \]

15393

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

15394

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

15395

\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+5 y = 0 \]

15396

\[ {}3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 0 \]

15397

\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y = 0 \]

15398

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

15399

\[ {}x^{2} y^{\prime \prime }-11 x y^{\prime }+36 y = 0 \]

15400

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

15401

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

15402

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0 \]

15537

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \]

15540

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \]

15545

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \]

15546

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

15548

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

15551

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \]

15553

\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-30 y = 0 \]

15556

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

15558

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

15559

\[ {}9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

15563

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

15598

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

15785

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

15800

\[ {}x^{2} y^{\prime \prime }-12 x y^{\prime }+42 y = 0 \]

15801

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

15826

\[ {}t^{2} y^{\prime \prime }-12 t y^{\prime }+42 y = 0 \]

15827

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

15846

\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-16 y = 0 \]

15847

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

15858

\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \]

16179

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

16183

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

16184

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

16189

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

16196

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

16197

\[ {}t^{2} y^{\prime \prime }+6 t y^{\prime }+6 y = 0 \]

16198

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

16199

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

16201

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

16202

\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (36 t^{2}-1\right ) y = 0 \]

16203

\[ {}t y^{\prime \prime }+2 y^{\prime }+16 t y = 0 \]

16204

\[ {}y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0 \]

16205

\[ {}y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0 \]

16240

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

16241

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

16359

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