4.26.21 Problems 2001 to 2100

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

#

ODE

Mathematica

Maple

Sympy

14270

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

14271

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

14409

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

14413

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

14909

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

15131

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

15134

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

15135

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

15165

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

15184

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

15185

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

15195

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

15196

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

15197

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

15198

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

15199

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

15200

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

15202

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

15203

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

15204

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

15205

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

15206

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

15221

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

15222

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

15223

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

15224

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

15225

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

15226

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

15227

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

15300

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

15301

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

15302

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

15303

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

15304

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

15305

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

15306

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

15307

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

15308

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

15309

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

15310

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

15311

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

15312

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

15313

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

15314

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

15315

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

15316

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

15317

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

15318

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

15319

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

15320

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

15321

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

15322

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

15323

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

15458

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

15461

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

15466

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

15467

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

15469

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

15472

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

15474

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

15477

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

15479

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

15480

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

15484

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

15519

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

15706

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

15721

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

15722

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

15747

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

15748

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

15767

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

15768

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

15779

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

16100

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

16104

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

16105

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

16110

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

16117

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

16118

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

16119

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

16120

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

16122

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

16123

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

16124

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

16125

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

16161

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

16162

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

16280

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

16282

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

16284

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

16361

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

16362

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

16363

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

16364

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

16365

\[ {} 4 x^{2} y^{\prime \prime }+17 y = 0 \]

16366

\[ {} 9 x^{2} y^{\prime \prime }-9 x y^{\prime }+10 y = 0 \]

16367

\[ {} 2 x^{2} y^{\prime \prime }-2 x y^{\prime }+20 y = 0 \]

16368

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0 \]

16369

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

16370

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