4.24.33 Problems 3201 to 3300

Table 4.1075: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

15426

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = \frac {5}{x^{3}} \]

15427

\[ {} 2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {50}{x^{3}} \]

15428

\[ {} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 85 \cos \left (2 \ln \left (x \right )\right ) \]

15429

\[ {} x^{2} y^{\prime \prime }-2 y = 15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right ) \]

15430

\[ {} 3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 4 x^{3} \]

15431

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

15432

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 6 x^{3} \]

15433

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 64 \ln \left (x \right ) x^{2} \]

15434

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

15440

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

15441

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 12 x^{3} \]

15442

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

15443

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \ln \left (x \right ) \]

15444

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

15445

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

15446

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

15447

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

15448

\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = \frac {10}{x} \]

15451

\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = x^{3} \]

15452

\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = {\mathrm e}^{-x^{2}} \]

15455

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 x y^{\prime }+9 y = 12 x \sin \left (x^{2}\right ) \]

15458

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

15461

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

15462

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

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

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

15471

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

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

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

15490

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

15493

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 18 \ln \left (x \right ) \]

15495

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

15497

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

15498

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 6 \]

15499

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

15504

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{\left (1+x \right )^{2}} \]

15505

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

15519

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

15706

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

15707

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

15708

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

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

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

15922

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

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

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

16169

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

16170

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

16275

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

16276

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

16277

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

16280

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

16281

\[ {} t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y = t^{3}+2 t \]

16282

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

16283

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

16284

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

16285

\[ {} 4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{{3}/{2}} \]

16286

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

16287

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

16326

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

16357

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

16358

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

16359

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

16360

\[ {} t y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime } = \frac {45}{8 t^{{7}/{2}}} \]

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

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

16371

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

16372

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

16373

\[ {} x^{3} y^{\prime \prime \prime }+22 x^{2} y^{\prime \prime }+124 x y^{\prime }+140 y = 0 \]

16374

\[ {} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }-46 x y^{\prime }+100 y = 0 \]