5.26.22 Problems 2101 to 2200

Table 5.1161: Second order, Linear, Homogeneous and non-constant coefficients

#

ODE

Mathematica

Maple

16361

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

16363

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

16440

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

16441

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

16442

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

16443

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

16444

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

16445

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

16446

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

16447

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

16448

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

16449

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

16450

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

16451

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

16470

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

16471

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

16472

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

16473

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

16482

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

16483

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

16484

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

16489

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

16491

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

16493

\[ {}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0 \]

16494

\[ {}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (4 x^{2}-4\right ) y = 0 \]

16495

\[ {}\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0 \]

16496

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

16498

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

16499

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

16506

\[ {}6 x^{2} y^{\prime \prime }+5 x y^{\prime }-y = 0 \]

16561

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

16562

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

16603

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

16606

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

16607

\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y = 0 \]

16608

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

16609

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

16610

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

16611

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

16612

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+25 y = 0 \]

16920

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

16921

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

16922

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

16924

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

17117

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

17118

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

17119

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

17120

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

17121

\[ {}\left (x +2\right )^{2} y^{\prime \prime }+3 \left (x +2\right ) y^{\prime }-3 y = 0 \]

17122

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

17135

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

17136

\[ {}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y = 0 \]

17138

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

17139

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

17140

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

17195

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

17216

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x^{2}-\frac {1}{9}\right ) y = 0 \]

17217

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

17218

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

17219

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

17220

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

17221

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

17222

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

17223

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

17545

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

17547

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

17548

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

17560

\[ {}y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+3 \ln \left (t \right ) y = 0 \]

17561

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

17562

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

17563

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

17565

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

17569

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

17570

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

17573

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

17574

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

17575

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

17576

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

17577

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

17578

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

17579

\[ {}x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0 \]

17580

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

17581

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

17582

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

17626

\[ {}a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = 0 \]

17627

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

17628

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

17629

\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+\frac {5 y}{4} = 0 \]

17630

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

17631

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

17632

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

17633

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

17634

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

17635

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

17636

\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+17 y = 0 \]

17637

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

17638

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

17995

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

17996

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

17997

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