4.26.21 Problems 2001 to 2100

Table 4.1153: Second order, Linear, Homogeneous and non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

14249

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

14256

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

14257

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

14258

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

14274

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

14275

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

14276

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

14277

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

14278

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

14279

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

14417

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

14421

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

14917

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

15139

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

15142

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

15143

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

15173

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

15192

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

15193

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

15203

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

15204

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

15205

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

15206

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

15207

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

15208

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

15210

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

15211

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

15212

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

15213

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

15214

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

15229

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

15230

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

15231

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

15232

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

15233

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

15234

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

15235

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

15308

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

15309

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

15310

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

15311

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

15312

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

15313

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

15314

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

15315

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

15316

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

15317

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

15318

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

15319

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

15320

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

15321

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

15322

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

15323

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

15324

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

15325

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

15326

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

15327

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

15328

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

15329

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

15330

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

15331

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

15466

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

15469

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

15474

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

15475

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

15477

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

15480

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

15482

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

15485

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

15487

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

15488

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

15492

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

15527

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

15714

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

15729

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

15730

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

15755

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

15756

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

15775

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

15776

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

15787

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

16108

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

16112

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

16113

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

16118

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

16125

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

16126

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

16127

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

16128

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

16130

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

16131

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

16132

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

16133

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

16169

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

16170

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

16288

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

16290

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

16292

\[ {} 4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 0 \]

16369

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

16370

\[ {} 3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0 \]