2.3.126 Problems 12501 to 12600

Table 2.835: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12501

2589

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x&=0 \end {array} \]

1.484

12502

2765

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -a&=0 \end {array} \]

1.484

12503

3901

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -l y&=0 \end {array} \]

1.484

12504

8250

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -v \left (v +1\right ) y&=0 \end {array} \]

1.484

12505

20758

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x -\left (v +2\right ) \left (v -1\right ) y&=0 \end {array} \]

1.484

12506

14862

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }-\left (1+3 x \right ) y^{\prime }-\left (x^{2}-x \right ) y&=0 \end {array} \]

1.485

12507

19613

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+1\right ) y&=0 \end {array} \]

1.485

12508

22256

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+2 \left (n +1\right ) x y^{\prime }-\left (v +n +1\right ) \left (v -n \right ) y&=0 \end {array} \]

1.485

12509

8999

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }-2 \left (n -1\right ) x y^{\prime }-\left (v -n +1\right ) \left (v +n \right ) y&=0 \end {array} \]

1.487

12510

9516

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }-2 \left (v -1\right ) x y^{\prime }-2 v y&=0 \end {array} \]

1.487

12511

18961

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+2 a x y^{\prime }+a \left (-1+a \right ) y&=0 \end {array} \]

1.487

12512

19065

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{2}+c x +d \right ) y&=0 \end {array} \]

1.487

12513

5754

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \end {array} \]

1.488

12514

9648

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-a^{2}+x^{2}\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \end {array} \]

1.488

12515

12502

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +1\right ) y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+y&=0 \end {array} \]

1.488

12516

17488

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \end {array} \]

1.488

12517

18356

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+\left (3 x +2\right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \end {array} \]

1.488

12518

22176

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+x -2\right ) y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }-\left (6 x^{2}+7 x \right ) y&=0 \end {array} \]

1.488

12519

23616

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-1+x \right ) y^{\prime \prime }+a y^{\prime }-2 y&=0 \end {array} \]

1.488

12520

12736

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-1+x \right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }-v \left (v +1\right ) y&=0 \end {array} \]

1.489

12521

20741

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-1+x \right ) y^{\prime \prime }+\left (\left (1+a \right ) x +b \right ) y^{\prime }&=0 \end {array} \]

1.489

12522

24558

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-1+x \right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y&=0 \end {array} \]

1.489

12523

2759

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-1+x \right ) y^{\prime \prime }+\left (\left (1+a \right ) x +b \right ) y^{\prime }-l y&=0 \end {array} \]

1.490

12524

6067

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (-1+x \right ) y^{\prime \prime }+\left (\left (\operatorname {a1} +\operatorname {b1} +1\right ) x -\operatorname {d1} \right ) y^{\prime }+\operatorname {a1} \operatorname {b1} \operatorname {d1}&=0 \end {array} \]

1.490

12525

24644

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (2+x \right ) y^{\prime \prime }+2 \left (n +1+\left (n +1-2 l \right ) x -l \,x^{2}\right ) y^{\prime }+\left (2 l \left (p -n -1\right ) x +2 p l +m \right ) y&=0 \end {array} \]

1.490

12526

9503

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right )^{2} y^{\prime \prime }+\left (x^{2}+x -1\right ) y^{\prime }-\left (2+x \right ) y&=0 \end {array} \]

1.491

12527

9593

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{{7}/{3}}&=0 \end {array} \]

1.491

12528

28024

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (2 x +3\right ) y+\left (x^{2}+x +1\right ) y^{\prime }+\left (x^{2}+3 x +4\right ) y^{\prime \prime }&=0 \end {array} \]

1.491

12529

3512

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-1+x \right ) \left (x -2\right ) y^{\prime \prime }-\left (2 x -3\right ) y^{\prime }+y&=0 \end {array} \]

1.492

12530

22203

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }-3 y&=0 \end {array} \]

1.492

12531

24689

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-\left (2 x^{2}+l -5 x \right ) y^{\prime }-\left (4 x -1\right ) y&=0 \end {array} \]

1.492

12532

6547

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \left (-1+x \right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }+\left (a x +b \right ) y&=0 \end {array} \]

1.493

12533

15295

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \left (-1+x \right ) y^{\prime \prime }+\left (\left (2 v +5\right ) x -2 v -3\right ) y^{\prime }+\left (v +1\right ) y&=0 \end {array} \]

1.493

12534

2443

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x^{2}+6 x +4\right ) y^{\prime \prime }+\left (10 x^{2}+21 x +8\right ) y^{\prime }+\left (12 x^{2}+17 x +8\right ) y&=0 \end {array} \]

1.494

12535

11282

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+y&=0 \end {array} \]

1.494

12536

14699

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (4 a^{2} x^{2}+1\right ) y+4 x^{2} y^{\prime \prime }&=0 \end {array} \]

1.494

12537

3908

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-\left (-4 k x +4 m^{2}+x^{2}-1\right ) y&=0 \end {array} \]

1.495

12538

15527

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (-v^{2}+x \right ) y&=0 \end {array} \]

1.496

12539

9061

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (-x^{2}+2 \left (1-m +2 l \right ) x -m^{2}+1\right ) y&=0 \end {array} \]

1.497

12540

20003

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (4 x^{2}+1\right ) y-4 \sqrt {x^{3}}\, {\mathrm e}^{x}&=0 \end {array} \]

1.497

12541

6183

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (a \,x^{2}+1\right ) y&=0 \end {array} \]

1.498

12542

6032

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +f \left (x \right ) y&=0 \end {array} \]

1.499

12543

14881

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+5 y^{\prime } x -y-\ln \left (x \right )&=0 \end {array} \]

1.499

12544

1629

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x -\left (4 x^{2}+12 x +3\right ) y&=0 \end {array} \]

1.500

12545

3688

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 x \left (2 x -1\right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \end {array} \]

1.500

12546

9843

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+6\right ) \left (x^{2}-4\right ) y&=0 \end {array} \]

1.500

12547

19889

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+4 x^{2} \ln \left (x \right ) y^{\prime }+\left (x^{2} \ln \left (x \right )^{2}+2 x -8\right ) y-4 x^{2} \sqrt {{\mathrm e}^{x} x^{-x}}&=0 \end {array} \]

1.500

12548

16875

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1&=0 \end {array} \]

1.501

12549

18185

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (4 x -1\right ) y^{\prime \prime }+\left (\left (4 a +2\right ) x -a \right ) y^{\prime }+a \left (-1+a \right ) y&=0 \end {array} \]

1.501

12550

21951

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (3 x -1\right )^{2} y^{\prime \prime }+3 \left (3 x -1\right ) y^{\prime }-9 y-\ln \left (3 x -1\right )^{2}&=0 \end {array} \]

1.501

12551

23081

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x \left (-1+x \right ) y^{\prime \prime }+3 \left (2 x -1\right ) y^{\prime }-20 y&=0 \end {array} \]

1.501

12552

28068

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (4 x +3\right ) y+16 x^{2} y^{\prime \prime }&=0 \end {array} \]

1.501

12553

4580

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (5+4 x \right ) y+32 y^{\prime } x +16 x^{2} y^{\prime \prime }&=0 \end {array} \]

1.502

12554

13300

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (27 x^{2}+4\right ) y^{\prime \prime }+27 y^{\prime } x -3 y&=0 \end {array} \]

1.502

12555

18267

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 48 x \left (-1+x \right ) y^{\prime \prime }+\left (152 x -40\right ) y^{\prime }+53 y&=0 \end {array} \]

1.502

12556

20204

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 50 x \left (-1+x \right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y&=0 \end {array} \]

1.502

12557

24580

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 144 x \left (-1+x \right ) y^{\prime \prime }+\left (120 x -48\right ) y^{\prime }+y&=0 \end {array} \]

1.502

12558

16869

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 144 x \left (-1+x \right ) y^{\prime \prime }+\left (168 x -96\right ) y^{\prime }+y&=0 \end {array} \]

1.503

12559

24671

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a \,x^{2} y^{\prime \prime }+b x y^{\prime }+\left (c \,x^{2}+d x +f \right ) y&=0 \end {array} \]

1.503

12560

23572

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \operatorname {a2} \,x^{2} y^{\prime \prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x \right ) y^{\prime }+\left (\operatorname {a0} \,x^{2}+\operatorname {b0} x +\operatorname {c0} \right ) y&=0 \end {array} \]

1.504

12561

24638

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a \,x^{2}+1\right ) y^{\prime \prime }+a x y^{\prime }+b y&=0 \end {array} \]

1.504

12562

25407

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime }&=0 \end {array} \]

1.504

12563

27935

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a^{2} x^{2}-1\right ) y^{\prime \prime }+2 a^{2} x y^{\prime }-2 a^{2} y&=0 \end {array} \]

1.504

12564

9474

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a \,x^{2}+b x \right ) y^{\prime \prime }+2 b y^{\prime }-2 a y&=0 \end {array} \]

1.505

12565

14705

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \operatorname {A2} \left (a x +b \right )^{2} y^{\prime \prime }+\operatorname {A1} \left (a x +b \right ) y^{\prime }+\operatorname {A0} \left (a x +b \right ) y&=0 \end {array} \]

1.505

12566

17854

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (d x +f \right ) y^{\prime }+g y&=0 \end {array} \]

1.505

12567

20773

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+y^{\prime } x -\left (2 x +3\right ) y&=0 \end {array} \]

1.505

12568

21615

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+2 y^{\prime } x +x^{3} y^{\prime \prime }&=0 \end {array} \]

1.505

12569

923

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+x^{2} y^{\prime }+\left (a \,x^{2}+b x +a \right ) y&=0 \end {array} \]

1.506

12570

22767

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-2 y&=0 \end {array} \]

1.506

12571

156

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }-x^{2} y^{\prime }+y x -\ln \left (x \right )^{3}&=0 \end {array} \]

1.507

12572

1501

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+y x&=0 \end {array} \]

1.507

12573

6052

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+y x -1&=0 \end {array} \]

1.507

12574

6884

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (2 x^{2}+1\right ) y^{\prime }-v \left (v +1\right ) x y&=0 \end {array} \]

1.507

12575

8947

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (x^{2}-1\right ) y^{\prime }-2 y x&=0 \end {array} \]

1.507

12576

15305

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (2 \left (n +1\right ) x^{2}+2 n +1\right ) y^{\prime }-\left (v -n \right ) \left (v +n +1\right ) x y&=0 \end {array} \]

1.507

12577

3360

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}+1\right ) y^{\prime \prime }-\left (2 \left (n -1\right ) x^{2}+2 n -1\right ) y^{\prime }+\left (v +n \right ) \left (-v +n -1\right ) x y&=0 \end {array} \]

1.508

12578

4031

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime }+y a \,x^{3}&=0 \end {array} \]

1.508

12579

6219

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}-1\right ) y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }-y x&=0 \end {array} \]

1.508

12580

13793

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}-1\right ) y^{\prime \prime }+\left (3 x^{2}-1\right ) y^{\prime }+y x&=0 \end {array} \]

1.509

12581

16891

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}-1\right ) y^{\prime \prime }+\left (a \,x^{2}+b \right ) y^{\prime }+c x y&=0 \end {array} \]

1.509

12582

23617

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -6 y x -y^{\prime }+x \left (x^{2}+2\right ) y^{\prime \prime }&=0 \end {array} \]

1.509

12583

25284

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}-2\right ) y^{\prime \prime }-\left (x^{3}+3 x^{2}-2 x -2\right ) y^{\prime }+\left (x^{2}+4 x +2\right ) y&=0 \end {array} \]

1.509

12584

3249

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x +1\right ) y-x \left (2 x +1\right ) y^{\prime }+x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \end {array} \]

1.510

12585

6512

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x +1\right ) y^{\prime \prime }+2 x \left (3 x +2\right ) y^{\prime }&=0 \end {array} \]

1.510

12586

9510

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-\frac {2 \left (x -2\right ) y^{\prime }}{x \left (-1+x \right )}+\frac {2 \left (x +1\right ) y}{x^{2} \left (-1+x \right )} \end {array} \]

1.510

12587

16986

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {\left (5 x -4\right ) y^{\prime }}{x \left (-1+x \right )}-\frac {\left (9 x -6\right ) y}{x^{2} \left (-1+x \right )} \end {array} \]

1.510

12588

24706

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-\frac {\left (\left (a +b +1\right ) x +\alpha +\beta -1\right ) y^{\prime }}{x \left (-1+x \right )}-\frac {\left (a b x -\alpha \beta \right ) y}{x^{2} \left (-1+x \right )} \end {array} \]

1.510

12589

25471

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-\frac {y^{\prime }}{x +1}-\frac {y}{x \left (x +1\right )^{2}} \end {array} \]

1.510

12590

3507

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {2 y^{\prime }}{x \left (x -2\right )}-\frac {y}{x^{2} \left (x -2\right )} \end {array} \]

1.511

12591

5518

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {2 y}{x \left (-1+x \right )^{2}} \end {array} \]

1.511

12592

8558

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-\frac {\left (\left (\alpha +\beta +1\right ) x^{2}-\left (\alpha +\beta +1+a \left (\gamma +\delta \right )-\delta \right ) x +a \gamma \right ) y^{\prime }}{x \left (-1+x \right ) \left (x -a \right )}-\frac {\left (\alpha \beta x -q \right ) y}{x \left (-1+x \right ) \left (x -a \right )} \end {array} \]

1.511

12593

19430

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-\frac {\left (A \,x^{2}+B x +C \right ) y^{\prime }}{\left (x -a \right ) \left (x -b \right ) \left (x -c \right )}-\frac {\left (\operatorname {DD} x +E \right ) y}{\left (x -a \right ) \left (x -b \right ) \left (x -c \right )} \end {array} \]

1.511

12594

6014

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {\left (x -4\right ) y^{\prime }}{2 x \left (x -2\right )}-\frac {\left (x -3\right ) y}{2 x^{2} \left (x -2\right )} \end {array} \]

1.512

12595

9377

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {y^{\prime }}{x +1}-\frac {\left (1+3 x \right ) y}{4 x^{2} \left (x +1\right )} \end {array} \]

1.512

12596

12595

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (-1+x \right )}+\frac {v \left (v +1\right ) y}{4 x^{2}} \end {array} \]

1.512

12597

26734

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-\frac {\left (\left (1+a \right ) x -1\right ) y^{\prime }}{x \left (-1+x \right )}-\frac {\left (\left (a^{2}-b^{2}\right ) x +c^{2}\right ) y}{4 x^{2} \left (-1+x \right )} \end {array} \]

1.512

12598

3367

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-\frac {\left (3 x -1\right ) y^{\prime }}{2 x \left (-1+x \right )}-\frac {\left (a x +b \right ) y}{4 x \left (-1+x \right )^{2}} \end {array} \]

1.513

12599

12366

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-\frac {\left (1-3 x \right ) y}{\left (-1+x \right ) \left (2 x -1\right )^{2}} \end {array} \]

1.513

12600

22209

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-\frac {\left (3 x +a +2 b \right ) y^{\prime }}{2 \left (a +x \right ) \left (x +b \right )}-\frac {\left (a -b \right ) y}{4 \left (a +x \right )^{2} \left (x +b \right )} \end {array} \]

1.513