Chapter 1
Lookup tables for all problems in current book

1.1 section 1
1.2 section 2. Solution found using all possible Kovacic cases
1.3 section 3. Problems from Kovacic related papers

1.1 section 1

Table 1.1: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

10461

1

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}

10462

2

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}

10463

3

\begin{align*} \left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y&=0 \\ \end{align*}

10464

4

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*}

10465

5

\begin{align*} 3 y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}

10466

6

\begin{align*} 5 y^{\prime \prime }-2 y^{\prime } x +10 y&=0 \\ \end{align*}

10467

7

\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*}

10468

8

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}

10469

9

\begin{align*} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ \end{align*}

10470

10

\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ \end{align*}

10471

11

\begin{align*} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \\ \end{align*}

10472

12

\begin{align*} t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{2} y&=0 \\ \end{align*}

10473

13

\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}

10474

14

\begin{align*} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}

10475

15

\begin{align*} \left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\ \end{align*}

10476

16

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

10477

17

\begin{align*} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}

10478

18

\begin{align*} \left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\ \end{align*}

10479

19

\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}

10480

20

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ \end{align*}

10481

21

\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}

10482

22

\begin{align*} 2 y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*}

10483

23

\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}

10484

24

\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}

10485

25

\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}

10486

26

\begin{align*} \left (-x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}

10487

27

\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}

10488

28

\begin{align*} \left (-1+x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}

10489

29

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}

10490

31

\begin{align*} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (-2+2 x \right ) y&=0 \\ \end{align*}

10491

32

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \\ \end{align*}

10492

33

\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}

10493

34

\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y&=0 \\ \end{align*}

10494

35

\begin{align*} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}

10495

36

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}

10496

38

\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}

10497

39

\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=0 \\ \end{align*}

10498

40

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y&=0 \\ \end{align*}

10499

41

\begin{align*} x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y&=0 \\ \end{align*}

10500

42

\begin{align*} x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y&=0 \\ \end{align*}

10501

43

\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y&=0 \\ \end{align*}

10502

44

\begin{align*} \left (-1+x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}

10503

45

\begin{align*} 4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y&=0 \\ \end{align*}

10504

46

\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \\ \end{align*}

10505

47

\begin{align*} \left (x +2\right ) y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*}

10506

48

\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (-x +2\right ) y&=0 \\ \end{align*}

10507

49

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (6 x +4\right ) y&=0 \\ \end{align*}

10508

50

\begin{align*} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y&=0 \\ \end{align*}

10509

51

\begin{align*} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y&=0 \\ \end{align*}

10510

52

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +6 y&=0 \\ \end{align*}

10511

53

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}

10512

54

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +20 y&=0 \\ \end{align*}

10513

55

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x -12 y&=0 \\ \end{align*}

10514

56

\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\ \end{align*}

10515

57

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x -4 y&=0 \\ \end{align*}

10516

58

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x +28 y&=0 \\ \end{align*}

10517

59

\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}

10518

60

\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }-9 y^{\prime } x -6 y&=0 \\ \end{align*}

10519

61

\begin{align*} \left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \\ \end{align*}

10520

62

\begin{align*} y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y&=0 \\ \end{align*}

10521

63

\begin{align*} \left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \\ \end{align*}

10522

64

\begin{align*} \left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (1+x \right ) y^{\prime }+60 y&=0 \\ \end{align*}

10523

65

\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x&=0 \\ \end{align*}

10524

66

\begin{align*} \left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y&=0 \\ \end{align*}

10525

67

\begin{align*} y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y&=0 \\ \end{align*}

10526

68

\begin{align*} \left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\ \end{align*}

10527

69

\begin{align*} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\ \end{align*}

10528

70

\begin{align*} \left (1+3 x \right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}

10529

71

\begin{align*} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\ \end{align*}

10530

72

\begin{align*} \left (x +2\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y&=0 \\ \end{align*}

10531

73

\begin{align*} \left (x +4\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y&=0 \\ \end{align*}

10532

74

\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (1+x \right ) y^{\prime }+8 y&=0 \\ \end{align*}

10533

75

\begin{align*} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \\ \end{align*}

10534

76

\begin{align*} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y&=0 \\ \end{align*}

10535

77

\begin{align*} \left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (-x +2\right ) y&=0 \\ \end{align*}

10536

78

\begin{align*} y^{\prime \prime }+3 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}

10537

79

\begin{align*} \left (4 x +2\right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y&=0 \\ \end{align*}

10538

80

\begin{align*} y^{\prime \prime }-3 y^{\prime } x +\left (2 x^{2}+5\right ) y&=0 \\ \end{align*}

10539

81

\begin{align*} 2 y^{\prime \prime }+5 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}

10540

82

\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}

10541

83

\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}

10542

84

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}

10543

85

\begin{align*} 3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y&=0 \\ \end{align*}

10544

86

\begin{align*} 12 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y&=0 \\ \end{align*}

10545

87

\begin{align*} x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y&=0 \\ \end{align*}

10546

88

\begin{align*} 18 x^{2} \left (1+x \right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}

10547

89

\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}

10548

90

\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (5+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*}

10549

91

\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y&=0 \\ \end{align*}

10550

92

\begin{align*} 2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (1-2 x \right ) y&=0 \\ \end{align*}

10551

93

\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align*}

10552

94

\begin{align*} 2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align*}

10553

95

\begin{align*} x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (-3 x +1\right ) y^{\prime }+y&=0 \\ \end{align*}

10554

96

\begin{align*} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (1+x \right ) y&=0 \\ \end{align*}

10555

97

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align*}

10556

98

\begin{align*} x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (4 x +3\right ) y&=0 \\ \end{align*}

10557

99

\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}

10558

100

\begin{align*} x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\ \end{align*}

10559

101

\begin{align*} 8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}

10560

102

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y&=0 \\ \end{align*}

10561

103

\begin{align*} x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \\ \end{align*}

10562

104

\begin{align*} 4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\ \end{align*}

10563

105

\begin{align*} 3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y&=0 \\ \end{align*}

10564

106

\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\ \end{align*}

10565

107

\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\ \end{align*}

10566

108

\begin{align*} 2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\ \end{align*}

10567

109

\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x&=0 \\ \end{align*}

10568

110

\begin{align*} 2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y&=0 \\ \end{align*}

10569

111

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \\ \end{align*}

10570

112

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \\ \end{align*}

10571

113

\begin{align*} 9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}

10572

114

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}

10573

115

\begin{align*} 8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y&=0 \\ \end{align*}

10574

116

\begin{align*} 2 x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (-3 x +1\right ) y^{\prime }+y&=0 \\ \end{align*}

10575

117

\begin{align*} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\ \end{align*}

10576

118

\begin{align*} 28 x^{2} \left (-3 x +1\right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \\ \end{align*}

10577

119

\begin{align*} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \\ \end{align*}

10578

120

\begin{align*} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y&=0 \\ \end{align*}

10579

121

\begin{align*} 3 x^{2} \left (1+x \right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}

10580

122

\begin{align*} 4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y&=0 \\ \end{align*}

10581

123

\begin{align*} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\ \end{align*}

10582

124

\begin{align*} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align*}

10583

125

\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\ \end{align*}

10584

126

\begin{align*} x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}

10585

127

\begin{align*} 4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (1+x \right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}

10586

128

\begin{align*} x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y&=0 \\ \end{align*}

10587

129

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \\ \end{align*}

10588

130

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y&=0 \\ \end{align*}

10589

131

\begin{align*} 16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \\ \end{align*}

10590

132

\begin{align*} 9 x^{2} \left (1+x \right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \\ \end{align*}

10591

133

\begin{align*} 36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y&=0 \\ \end{align*}

10592

134

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (-x +3\right ) y^{\prime }+4 y&=0 \\ \end{align*}

10593

135

\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}

10594

136

\begin{align*} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}

10595

137

\begin{align*} 2 x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y&=0 \\ \end{align*}

10596

138

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \\ \end{align*}

10597

139

\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \\ \end{align*}

10598

140

\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y&=0 \\ \end{align*}

10599

141

\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}

10600

142

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \\ \end{align*}

10601

143

\begin{align*} 4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\ \end{align*}

10602

144

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y&=0 \\ \end{align*}

10603

145

\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\ \end{align*}

10604

146

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y&=0 \\ \end{align*}

10605

147

\begin{align*} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}

10606

148

\begin{align*} 3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}

10607

149

\begin{align*} 9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y&=0 \\ \end{align*}

10608

150

\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}

10609

151

\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (1+4 x \right ) y&=0 \\ \end{align*}

10610

152

\begin{align*} x \left (1+x \right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}

10611

153

\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y&=0 \\ \end{align*}

10612

154

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \\ \end{align*}

10613

155

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\ \end{align*}

10614

156

\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 y x&=0 \\ \end{align*}

10615

157

\begin{align*} 4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\ \end{align*}

10616

158

\begin{align*} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align*}

10617

159

\begin{align*} 9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (4 x +3\right ) y&=0 \\ \end{align*}

10618

160

\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y&=0 \\ \end{align*}

10619

161

\begin{align*} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \\ \end{align*}

10620

162

\begin{align*} x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (-3 x +4\right ) y^{\prime }+4 y&=0 \\ \end{align*}

10621

163

\begin{align*} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}

10622

164

\begin{align*} x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}

10623

165

\begin{align*} 9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y&=0 \\ \end{align*}

10624

166

\begin{align*} 2 x^{2} \left (x +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \\ \end{align*}

10625

167

\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \\ \end{align*}

10626

168

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \\ \end{align*}

10627

169

\begin{align*} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y&=0 \\ \end{align*}

10628

170

\begin{align*} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align*}

10629

171

\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y&=0 \\ \end{align*}

10630

172

\begin{align*} x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*}

10631

173

\begin{align*} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \\ \end{align*}

10632

174

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \\ \end{align*}

10633

175

\begin{align*} x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-3 \left (x +3\right ) y&=0 \\ \end{align*}

10634

176

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y&=0 \\ \end{align*}

10635

177

\begin{align*} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \\ \end{align*}

10636

178

\begin{align*} 3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \\ \end{align*}

10637

179

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y&=0 \\ \end{align*}

10638

180

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y&=0 \\ \end{align*}

10639

181

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \\ \end{align*}

10640

182

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y&=0 \\ \end{align*}

10641

183

\begin{align*} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y&=0 \\ \end{align*}

10642

184

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*}

10643

185

\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*}

10644

186

\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \\ \end{align*}

10645

187

\begin{align*} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y&=0 \\ \end{align*}

10646

188

\begin{align*} x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y&=0 \\ \end{align*}

10647

189

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y&=0 \\ \end{align*}

10648

190

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y&=0 \\ \end{align*}

10649

191

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \\ \end{align*}

10650

192

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \\ \end{align*}

10651

193

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y&=0 \\ \end{align*}

10652

194

\begin{align*} y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1}&=0 \\ \end{align*}

10653

195

\begin{align*} y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y&=0 \\ \end{align*}

10654

196

\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}

10655

197

\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}

10656

198

\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y&=0 \\ \end{align*}

10657

199

\begin{align*} \left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y&=0 \\ \end{align*}

10658

200

\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

10659

201

\begin{align*} y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1}&=0 \\ \end{align*}

10660

202

\begin{align*} y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y&=0 \\ \end{align*}

10661

204

\begin{align*} 2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\ \end{align*}

10662

205

\begin{align*} 2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y&=0 \\ \end{align*}

10663

206

\begin{align*} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\ \end{align*}

10664

207

\begin{align*} 2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\ \end{align*}

10665

208

\begin{align*} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\ \end{align*}

10666

209

\begin{align*} t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y&=0 \\ \end{align*}

10667

210

\begin{align*} t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y&=0 \\ \end{align*}

10668

211

\begin{align*} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\ \end{align*}

10669

212

\begin{align*} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\ \end{align*}

10670

213

\begin{align*} t y^{\prime \prime }+t y^{\prime }+2 y&=0 \\ \end{align*}

10671

214

\begin{align*} t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y&=0 \\ \end{align*}

10672

215

\begin{align*} t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}

10673

216

\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}

10674

217

\begin{align*} \left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+\lambda y&=0 \\ \end{align*}

10675

218

\begin{align*} 4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \\ \end{align*}

10676

219

\begin{align*} f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\ \end{align*}

10677

220

\begin{align*} z y^{\prime \prime }-2 y^{\prime }+y z&=0 \\ \end{align*}

10678

221

\begin{align*} z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}&=0 \\ \end{align*}

10679

222

\begin{align*} y^{\prime \prime }+2 y^{\prime } x +4 y&=0 \\ \end{align*}

10680

223

\begin{align*} y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*}

10681

224

\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*}

10682

225

\begin{align*} \left (-4 x^{2}+1\right ) y^{\prime \prime }-20 y^{\prime } x -16 y&=0 \\ \end{align*}

10683

226

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}

10684

227

\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (x +2\right ) y&=0 \\ \end{align*}

10685

228

\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\ \end{align*}

10686

229

\begin{align*} 4 y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ \end{align*}

10687

230

\begin{align*} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}

10688

231

\begin{align*} 4 x y^{\prime \prime }-y^{\prime } x +2 y&=0 \\ \end{align*}

10689

232

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\ \end{align*}

10690

233

\begin{align*} 3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \\ \end{align*}

10691

234

\begin{align*} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y&=0 \\ \end{align*}

10692

235

\begin{align*} 4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align*}

10693

236

\begin{align*} x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align*}

10694

237

\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\ \end{align*}

10695

238

\begin{align*} x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y&=0 \\ \end{align*}

10696

239

\begin{align*} x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \\ \end{align*}

10697

240

\begin{align*} x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\ \end{align*}

10698

241

\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align*}

10699

242

\begin{align*} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \\ \end{align*}

10700

243

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\ \end{align*}

10701

244

\begin{align*} x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \\ \end{align*}

10702

245

\begin{align*} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \\ \end{align*}

10703

246

\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \\ \end{align*}

10704

247

\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\ \end{align*}

10705

248

\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \\ \end{align*}

10706

249

\begin{align*} x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y&=0 \\ \end{align*}

10707

250

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\ \end{align*}

10708

251

\begin{align*} x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (1+x \right ) y&=0 \\ \end{align*}

10709

252

\begin{align*} x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}

10710

253

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y&=0 \\ \end{align*}

10711

254

\begin{align*} x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}

10712

255

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y&=0 \\ \end{align*}

10713

256

\begin{align*} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*}

10714

257

\begin{align*} 2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\ \end{align*}

10715

258

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

10716

259

\begin{align*} x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y&=0 \\ \end{align*}

10717

260

\begin{align*} x^{4} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}

10718

261

\begin{align*} x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y&=0 \\ \end{align*}

10719

262

\begin{align*} \left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \\ \end{align*}

10720

263

\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}

10721

264

\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}

10722

265

\begin{align*} x^{2} \left (1-4 x \right ) y^{\prime \prime }-\frac {y^{\prime } x}{2}-\frac {3 y x}{4}&=0 \\ \end{align*}

10723

266

\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\ \end{align*}

10724

267

\begin{align*} x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\ \end{align*}

10725

268

\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y&=0 \\ \end{align*}

10726

269

\begin{align*} 2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}&=0 \\ \end{align*}

10727

270

\begin{align*} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4}&=0 \\ \end{align*}

10728

271

\begin{align*} 2 x \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}

10729

272

\begin{align*} 2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \\ \end{align*}

10730

273

\begin{align*} x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \\ \end{align*}

10731

274

\begin{align*} 4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \\ \end{align*}

10732

275

\begin{align*} u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}

10733

276

\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}

10734

277

\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}

10735

278

\begin{align*} u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}

10736

279

\begin{align*} u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}

10737

280

\begin{align*} -a^{2} y+y^{\prime \prime }&=\frac {6 y}{x^{2}} \\ \end{align*}

10738

281

\begin{align*} y^{\prime \prime }+n^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}

10739

282

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\frac {1}{4}\right ) y&=0 \\ \end{align*}

10740

283

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}}&=0 \\ \end{align*}

10741

284

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {25}{4}\right ) y&=0 \\ \end{align*}

10742

285

\begin{align*} y^{\prime \prime }+q y^{\prime }&=\frac {2 y}{x^{2}} \\ \end{align*}

10743

286

\begin{align*} x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}

10744

287

\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}

10745

288

\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}

10746

289

\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

10747

290

\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

10748

291

\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\ \end{align*}

10749

292

\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\ \end{align*}

10750

293

\begin{align*} \left (2 x -3\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}

10751

294

\begin{align*} y^{\prime \prime }-y^{\prime } x -3 y&=0 \\ \end{align*}

10752

295

\begin{align*} y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

10753

296

\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}

10754

297

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}

10755

298

\begin{align*} x \left (1+x \right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (-1+x \right ) y&=0 \\ \end{align*}

10756

299

\begin{align*} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}

10757

300

\begin{align*} x y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ \end{align*}

10758

301

\begin{align*} x \left (-1+x \right )^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}

10759

302

\begin{align*} y^{\prime \prime }-2 y^{\prime } x +x^{2} y&=0 \\ \end{align*}

10760

303

\begin{align*} x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )&=0 \\ \end{align*}

10761

304

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+y^{\prime } x \right )&=0 \\ \end{align*}

10762

305

\begin{align*} \left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (-x +2\right ) x^{2} y^{\prime \prime }&=0 \\ \end{align*}

10763

306

\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \\ \end{align*}

10764

307

\begin{align*} 4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}

10765

309

\begin{align*} y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\ \end{align*}

10766

310

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\ \end{align*}

10767

311

\begin{align*} x \left (x +2\right ) y^{\prime \prime }+2 \left (1+x \right ) y^{\prime }-2 y&=0 \\ \end{align*}

10768

313

\begin{align*} x \left (x +2\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }-4 y&=0 \\ \end{align*}

10769

314

\begin{align*} \left (-1+x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}

10770

315

\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

10771

316

\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}

10772

317

\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}

10773

318

\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}

10774

319

\begin{align*} \left (x +2\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}

10775

320

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \\ \end{align*}

10776

321

\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\ \end{align*}

10777

322

\begin{align*} \left (-1+x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}

10778

325

\begin{align*} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\ \end{align*}

10779

326

\begin{align*} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}

10780

327

\begin{align*} 2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y&=0 \\ \end{align*}

10781

328

\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y&=0 \\ \end{align*}

10782

329

\begin{align*} x y^{\prime \prime }+2 y^{\prime }-y x&=0 \\ \end{align*}

10783

330

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

10784

331

\begin{align*} x y^{\prime \prime }+\left (-6+x \right ) y^{\prime }-3 y&=0 \\ \end{align*}

10785

332

\begin{align*} x^{4} y^{\prime \prime }+\lambda y&=0 \\ \end{align*}

10786

333

\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\ \end{align*}

10787

334

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

10788

335

\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align*}

10789

336

\begin{align*} x y^{\prime \prime }+3 y^{\prime }+x^{3} y&=0 \\ \end{align*}

10790

337

\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}

10791

338

\begin{align*} 16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y&=0 \\ \end{align*}

10792

339

\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

10793

340

\begin{align*} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y&=0 \\ \end{align*}

10794

341

\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}

10795

342

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}

10796

343

\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\ \end{align*}

10797

344

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y&=0 \\ \end{align*}

10798

345

\begin{align*} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*}

10799

346

\begin{align*} x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align*}

10800

347

\begin{align*} 2 x \left (-1+x \right ) y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y&=0 \\ \end{align*}

10801

348

\begin{align*} x y^{\prime \prime }+2 y^{\prime }+4 y x&=0 \\ \end{align*}

10802

349

\begin{align*} x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}

10803

350

\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}

10804

351

\begin{align*} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y&=0 \\ \end{align*}

10805

352

\begin{align*} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align*}

10806

353

\begin{align*} 4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}

10807

354

\begin{align*} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \\ \end{align*}

10808

355

\begin{align*} 3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\ \end{align*}

10809

356

\begin{align*} x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \\ \end{align*}

10810

357

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4}&=0 \\ \end{align*}

10811

358

\begin{align*} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y&=0 \\ \end{align*}

10812

359

\begin{align*} y-\left (1+x \right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}

10813

360

\begin{align*} x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}

10814

361

\begin{align*} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y&=0 \\ \end{align*}

10815

362

\begin{align*} 2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y&=0 \\ \end{align*}

10816

363

\begin{align*} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*}

10817

364

\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \\ \end{align*}

10818

365

\begin{align*} u^{\prime \prime }+\frac {u}{x^{2}}&=0 \\ \end{align*}

10819

366

\begin{align*} u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u&=0 \\ \end{align*}

10820

367

\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\ \end{align*}

10821

368

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}

10822

369

\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (1+x \right )^{2}}&=0 \\ \end{align*}

10823

370

\begin{align*} y^{\prime \prime }+\frac {y}{2 x^{4}}&=0 \\ \end{align*}

10824

371

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

10825

372

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

10826

373

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

10827

374

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

10828

375

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

10829

376

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

10830

377

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

10831

378

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

10832

379

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

10833

380

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

10834

381

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

10835

382

\begin{align*} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*}

10836

383

\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y x&=0 \\ \end{align*}

10837

384

\begin{align*} x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align*}

10838

385

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}

10839

388

\begin{align*} x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}

10840

389

\begin{align*} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\ \end{align*}

10841

390

\begin{align*} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align*}

10842

391

\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}

10843

392

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

10844

394

\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y&=0 \\ \end{align*}

10845

395

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

10846

396

\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y&=0 \\ \end{align*}

10847

398

\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}

10848

399

\begin{align*} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\ \end{align*}

10849

400

\begin{align*} x^{3} y^{\prime \prime }+y^{\prime }-\frac {y}{x}&=0 \\ \end{align*}

10850

401

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

10851

402

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \\ \end{align*}

10852

404

\begin{align*} y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}

10853

405

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}

10854

406

\begin{align*} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}

10855

407

\begin{align*} \left (1+x \right ) y^{\prime \prime }-\left (x +2\right ) y^{\prime }+y&=0 \\ \end{align*}

10856

408

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}

10857

409

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}

10858

410

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

10859

411

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}

10860

412

\begin{align*} \left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y&=0 \\ \end{align*}

10861

413

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*}

10862

414

\begin{align*} 3 y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}

10863

415

\begin{align*} 5 y^{\prime \prime }-2 y^{\prime } x +10 y&=0 \\ \end{align*}

10864

416

\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*}

10865

417

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}

10866

418

\begin{align*} y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ \end{align*}

10867

419

\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ \end{align*}

10868

420

\begin{align*} \left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y&=0 \\ \end{align*}

10869

421

\begin{align*} t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y&=0 \\ \end{align*}

10870

422

\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}

10871

423

\begin{align*} \left (-1+x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}

10872

424

\begin{align*} x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y&=0 \\ \end{align*}

10873

425

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

10874

426

\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \\ \end{align*}

10875

427

\begin{align*} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}

10876

428

\begin{align*} \left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\ \end{align*}

10877

429

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

10878

430

\begin{align*} t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}

10879

431

\begin{align*} \left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\ \end{align*}

10880

432

\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}

10881

433

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ \end{align*}

10882

434

\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}

10883

435

\begin{align*} 2 y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*}

10884

436

\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}

10885

437

\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}

10886

438

\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}

10887

439

\begin{align*} \left (-x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}

10888

440

\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}

10889

441

\begin{align*} \left (-1+x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}

10890

442

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}

10891

444

\begin{align*} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (-2+2 x \right ) y&=0 \\ \end{align*}

10892

445

\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y&=0 \\ \end{align*}

10893

446

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \\ \end{align*}

10894

447

\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}

10895

448

\begin{align*} x^{2} y^{\prime \prime }+2 x \left (-1+x \right ) y^{\prime }+\left (x^{2}-2 x +2\right ) y&=0 \\ \end{align*}

10896

449

\begin{align*} x^{2} y^{\prime \prime }-x \left (2 x -1\right ) y^{\prime }+\left (x^{2}-x -1\right ) y&=0 \\ \end{align*}

10897

450

\begin{align*} \left (1-2 x \right ) y^{\prime \prime }+2 y^{\prime }+\left (2 x -3\right ) y&=0 \\ \end{align*}

10898

451

\begin{align*} 2 x y^{\prime \prime }+\left (1+4 x \right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align*}

10899

452

\begin{align*} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align*}

10900

453

\begin{align*} 4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y&=0 \\ \end{align*}

10901

454

\begin{align*} x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}

10902

455

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}

10903

456

\begin{align*} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}

10904

457

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}

10905

458

\begin{align*} x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y&=0 \\ \end{align*}

10906

460

\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}

10907

461

\begin{align*} \left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (1+x \right ) y&=0 \\ \end{align*}

10908

462

\begin{align*} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (-2+2 x \right ) y&=0 \\ \end{align*}

10909

463

\begin{align*} x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y&=0 \\ \end{align*}

10910

464

\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \\ \end{align*}

10911

465

\begin{align*} \left (1+x \right )^{2} y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }-\left (x^{2}+2 x -1\right ) y&=0 \\ \end{align*}

10912

466

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \\ \end{align*}

10913

467

\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}

10914

468

\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-2 y^{\prime }-\left (2 x +3\right ) y&=0 \\ \end{align*}

10915

469

\begin{align*} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}

10916

470

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}

10917

472

\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y&=0 \\ \end{align*}

10918

473

\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=0 \\ \end{align*}

10919

474

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y&=0 \\ \end{align*}

10920

475

\begin{align*} x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y&=0 \\ \end{align*}

10921

476

\begin{align*} x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y&=0 \\ \end{align*}

10922

477

\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y&=0 \\ \end{align*}

10923

478

\begin{align*} \left (-1+x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}

10924

479

\begin{align*} 4 x^{2} y^{\prime \prime }-4 x \left (1+x \right ) y^{\prime }+\left (2 x +3\right ) y&=0 \\ \end{align*}

10925

480

\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }-\left (6 x -8\right ) y&=0 \\ \end{align*}

10926

481

\begin{align*} \left (x +2\right ) y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*}

10927

482

\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (-x +2\right ) y&=0 \\ \end{align*}

10928

483

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (6 x +4\right ) y&=0 \\ \end{align*}

10929

484

\begin{align*} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y&=0 \\ \end{align*}

10930

485

\begin{align*} x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+2 x \left (x^{2}+5\right ) y^{\prime }+2 \left (-x^{2}+3\right ) y&=0 \\ \end{align*}

10931

486

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +6 y&=0 \\ \end{align*}

10932

487

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}

10933

488

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x +20 y&=0 \\ \end{align*}

10934

489

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x -12 y&=0 \\ \end{align*}

10935

490

\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\ \end{align*}

10936

491

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x -4 y&=0 \\ \end{align*}

10937

492

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x +28 y&=0 \\ \end{align*}

10938

493

\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}

10939

495

\begin{align*} \left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (x -2\right ) y^{\prime }+36 y&=0 \\ \end{align*}

10940

496

\begin{align*} y^{\prime \prime }+\left (x -3\right ) y^{\prime }+3 y&=0 \\ \end{align*}

10941

497

\begin{align*} \left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \\ \end{align*}

10942

498

\begin{align*} \left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (1+x \right ) y^{\prime }+60 y&=0 \\ \end{align*}

10943

499

\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x&=0 \\ \end{align*}

10944

500

\begin{align*} \left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y&=0 \\ \end{align*}

10945

501

\begin{align*} y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y&=0 \\ \end{align*}

10946

502

\begin{align*} \left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \\ \end{align*}

10947

503

\begin{align*} y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y&=0 \\ \end{align*}

10948

504

\begin{align*} \left (1+3 x \right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}

10949

505

\begin{align*} \left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y&=0 \\ \end{align*}

10950

506

\begin{align*} \left (x +2\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y&=0 \\ \end{align*}

10951

507

\begin{align*} \left (x +4\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y&=0 \\ \end{align*}

10952

508

\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (1+x \right ) y^{\prime }+8 y&=0 \\ \end{align*}

10953

509

\begin{align*} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \\ \end{align*}

10954

510

\begin{align*} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (1+7 x \right ) y^{\prime }+2 y&=0 \\ \end{align*}

10955

511

\begin{align*} \left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (-x +2\right ) y&=0 \\ \end{align*}

10956

512

\begin{align*} y^{\prime \prime }+3 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}

10957

513

\begin{align*} \left (4 x +2\right ) y^{\prime \prime }-4 y^{\prime }-\left (6+4 x \right ) y&=0 \\ \end{align*}

10958

514

\begin{align*} y^{\prime \prime }-3 y^{\prime } x +\left (2 x^{2}+5\right ) y&=0 \\ \end{align*}

10959

515

\begin{align*} 2 y^{\prime \prime }+5 y^{\prime } x +\left (2 x^{2}+4\right ) y&=0 \\ \end{align*}

10960

516

\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}

10961

517

\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}

10962

518

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}

10963

519

\begin{align*} 3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y&=0 \\ \end{align*}

10964

520

\begin{align*} 12 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y&=0 \\ \end{align*}

10965

521

\begin{align*} y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\ \end{align*}

10966

522

\begin{align*} 18 x^{2} \left (1+x \right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}

10967

523

\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}

10968

524

\begin{align*} 2 x^{2} y^{\prime \prime }+x \left (5+x \right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*}

10969

525

\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y&=0 \\ \end{align*}

10970

526

\begin{align*} 2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (1-2 x \right ) y&=0 \\ \end{align*}

10971

527

\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align*}

10972

528

\begin{align*} 2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align*}

10973

529

\begin{align*} x^{2} \left (x +4\right ) y^{\prime \prime }-x \left (-3 x +1\right ) y^{\prime }+y&=0 \\ \end{align*}

10974

530

\begin{align*} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (1+x \right ) y&=0 \\ \end{align*}

10975

531

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align*}

10976

532

\begin{align*} x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (4 x +3\right ) y&=0 \\ \end{align*}

10977

533

\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}

10978

534

\begin{align*} x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\ \end{align*}

10979

535

\begin{align*} 8 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}

10980

536

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y&=0 \\ \end{align*}

10981

537

\begin{align*} x \left (x^{2}+3\right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-8 y x&=0 \\ \end{align*}

10982

538

\begin{align*} 4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y&=0 \\ \end{align*}

10983

539

\begin{align*} 3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y&=0 \\ \end{align*}

10984

540

\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y&=0 \\ \end{align*}

10985

541

\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\ \end{align*}

10986

542

\begin{align*} 2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y&=0 \\ \end{align*}

10987

543

\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x&=0 \\ \end{align*}

10988

544

\begin{align*} 2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y&=0 \\ \end{align*}

10989

545

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y&=0 \\ \end{align*}

10990

546

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (6 x^{2}+1\right ) y^{\prime }+\left (9 x^{2}+1\right ) y&=0 \\ \end{align*}

10991

547

\begin{align*} 9 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+3\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}

10992

548

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-25 x^{2}+1\right ) y&=0 \\ \end{align*}

10993

549

\begin{align*} 8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y&=0 \\ \end{align*}

10994

550

\begin{align*} 2 x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (-3 x +1\right ) y^{\prime }+y&=0 \\ \end{align*}

10995

551

\begin{align*} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\ \end{align*}

10996

552

\begin{align*} 28 x^{2} \left (-3 x +1\right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \\ \end{align*}

10997

553

\begin{align*} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \\ \end{align*}

10998

554

\begin{align*} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }-4 x \left (-3 x^{2}-3 x +1\right ) y^{\prime }+3 \left (x^{2}-x +1\right ) y&=0 \\ \end{align*}

10999

555

\begin{align*} 3 x^{2} \left (1+x \right )^{2} y^{\prime \prime }-x \left (-11 x^{2}-10 x +1\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}

11000

556

\begin{align*} 4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y&=0 \\ \end{align*}

11001

557

\begin{align*} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\ \end{align*}

11002

558

\begin{align*} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align*}

11003

559

\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-2 x \left (2 x^{2}+1\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\ \end{align*}

11004

560

\begin{align*} x^{2} y^{\prime \prime }-x \left (5-x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}

11005

561

\begin{align*} 4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (1+x \right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}

11006

562

\begin{align*} x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }-x \left (-2 x^{2}-4 x +1\right ) y^{\prime }+y&=0 \\ \end{align*}

11007

563

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-2 x^{2}+3 x +5\right ) y^{\prime }+\left (-14 x^{2}+12 x +1\right ) y&=0 \\ \end{align*}

11008

564

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y&=0 \\ \end{align*}

11009

565

\begin{align*} 16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y&=0 \\ \end{align*}

11010

566

\begin{align*} 9 x^{2} \left (1+x \right ) y^{\prime \prime }+3 x \left (-x^{2}+11 x +5\right ) y^{\prime }+\left (-7 x^{2}+16 x +1\right ) y&=0 \\ \end{align*}

11011

567

\begin{align*} 36 x^{2} \left (1-2 x \right ) y^{\prime \prime }+24 x \left (1-9 x \right ) y^{\prime }+\left (1-70 x \right ) y&=0 \\ \end{align*}

11012

568

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (-x +3\right ) y^{\prime }+4 y&=0 \\ \end{align*}

11013

569

\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y&=0 \\ \end{align*}

11014

570

\begin{align*} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}

11015

571

\begin{align*} 2 x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (6-x \right ) y^{\prime }+\left (8-x \right ) y&=0 \\ \end{align*}

11016

572

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \\ \end{align*}

11017

573

\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5+4 x \right ) y^{\prime }+\left (9+4 x \right ) y&=0 \\ \end{align*}

11018

574

\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y&=0 \\ \end{align*}

11019

575

\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}

11020

576

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-3 x \left (-x^{2}+1\right ) y^{\prime }+4 y&=0 \\ \end{align*}

11021

577

\begin{align*} 4 x^{2} y^{\prime \prime }+2 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\ \end{align*}

11022

578

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+1\right ) y^{\prime }+y&=0 \\ \end{align*}

11023

579

\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+7 x^{3} y^{\prime }+\left (3 x^{2}+1\right ) y&=0 \\ \end{align*}

11024

580

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-4 x^{2}+1\right ) y^{\prime }+\left (2 x^{2}+1\right ) y&=0 \\ \end{align*}

11025

581

\begin{align*} 4 x^{2} \left (x^{2}+4\right ) y^{\prime \prime }+3 x \left (3 x^{2}+8\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y&=0 \\ \end{align*}

11026

582

\begin{align*} 3 x^{2} \left (x^{2}+3\right ) y^{\prime \prime }+x \left (11 x^{2}+3\right ) y^{\prime }+\left (5 x^{2}+1\right ) y&=0 \\ \end{align*}

11027

583

\begin{align*} 9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y&=0 \\ \end{align*}

11028

584

\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}

11029

585

\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 y^{\prime } x +\left (1+4 x \right ) y&=0 \\ \end{align*}

11030

586

\begin{align*} x \left (1+x \right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y&=0 \\ \end{align*}

11031

587

\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y&=0 \\ \end{align*}

11032

588

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \\ \end{align*}

11033

589

\begin{align*} 9 x^{2} y^{\prime \prime }+3 x \left (-x^{2}+1\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\ \end{align*}

11034

590

\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-8 y x&=0 \\ \end{align*}

11035

591

\begin{align*} 4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\ \end{align*}

11036

592

\begin{align*} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+8 x^{2} y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align*}

11037

593

\begin{align*} 9 x^{2} \left (x +3\right ) y^{\prime \prime }+3 x \left (3+7 x \right ) y^{\prime }+\left (4 x +3\right ) y&=0 \\ \end{align*}

11038

594

\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y&=0 \\ \end{align*}

11039

595

\begin{align*} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \\ \end{align*}

11040

596

\begin{align*} x^{2} \left (3 x +4\right ) y^{\prime \prime }-x \left (-3 x +4\right ) y^{\prime }+4 y&=0 \\ \end{align*}

11041

597

\begin{align*} 4 x^{2} \left (x^{2}+3 x +1\right ) y^{\prime \prime }+8 x^{2} \left (2 x +3\right ) y^{\prime }+\left (9 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}

11042

598

\begin{align*} x^{2} \left (1-x \right )^{2} y^{\prime \prime }-x \left (-3 x^{2}+2 x +1\right ) y^{\prime }+\left (x^{2}+1\right ) y&=0 \\ \end{align*}

11043

599

\begin{align*} 9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y&=0 \\ \end{align*}

11044

600

\begin{align*} 2 x^{2} \left (x +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \\ \end{align*}

11045

601

\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \\ \end{align*}

11046

602

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \\ \end{align*}

11047

603

\begin{align*} x^{2} \left (-2 x^{2}+1\right ) y^{\prime \prime }+x \left (-13 x^{2}+7\right ) y^{\prime }-14 x^{2} y&=0 \\ \end{align*}

11048

604

\begin{align*} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align*}

11049

605

\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y&=0 \\ \end{align*}

11050

606

\begin{align*} x^{2} y^{\prime \prime }+x \left (x +2\right ) y^{\prime }-\left (2-3 x \right ) y&=0 \\ \end{align*}

11051

607

\begin{align*} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \\ \end{align*}

11052

608

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \\ \end{align*}

11053

609

\begin{align*} x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-3 \left (x +3\right ) y&=0 \\ \end{align*}

11054

610

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y&=0 \\ \end{align*}

11055

611

\begin{align*} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \\ \end{align*}

11056

612

\begin{align*} 3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \\ \end{align*}

11057

613

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (1-10 x \right ) y^{\prime }-\left (9-10 x \right ) y&=0 \\ \end{align*}

11058

614

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }+3 x^{2} y^{\prime }-\left (6-x \right ) y&=0 \\ \end{align*}

11059

615

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \\ \end{align*}

11060

616

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y&=0 \\ \end{align*}

11061

617

\begin{align*} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (1+4 x \right ) y^{\prime }-\left (49+27 x \right ) y&=0 \\ \end{align*}

11062

618

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-2 x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*}

11063

619

\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \\ \end{align*}

11064

620

\begin{align*} x^{2} y^{\prime \prime }+x \left (2 x^{2}+1\right ) y^{\prime }-\left (-10 x^{2}+1\right ) y&=0 \\ \end{align*}

11065

621

\begin{align*} x^{2} y^{\prime \prime }+x \left (-2 x^{2}+1\right ) y^{\prime }-4 \left (2 x^{2}+1\right ) y&=0 \\ \end{align*}

11066

622

\begin{align*} x^{2} y^{\prime \prime }+x \left (-3 x^{2}+1\right ) y^{\prime }-4 \left (-3 x^{2}+1\right ) y&=0 \\ \end{align*}

11067

623

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 x^{2} y&=0 \\ \end{align*}

11068

624

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y&=0 \\ \end{align*}

11069

625

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \\ \end{align*}

11070

626

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \\ \end{align*}

11071

627

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y&=0 \\ \end{align*}

11072

628

\begin{align*} y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1}&=0 \\ \end{align*}

11073

629

\begin{align*} y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y&=0 \\ \end{align*}

11074

630

\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}

11075

631

\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y&=0 \\ \end{align*}

11076

632

\begin{align*} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y&=0 \\ \end{align*}

11077

633

\begin{align*} \left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y&=0 \\ \end{align*}

11078

634

\begin{align*} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

11079

635

\begin{align*} y^{\prime \prime }-\frac {2 t y^{\prime }}{t^{2}+1}+\frac {2 y}{t^{2}+1}&=0 \\ \end{align*}

11080

636

\begin{align*} y^{\prime \prime }+\left (t^{2}+2 t +1\right ) y^{\prime }-\left (4+4 t \right ) y&=0 \\ \end{align*}

11081

638

\begin{align*} 2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y&=0 \\ \end{align*}

11082

639

\begin{align*} 2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y&=0 \\ \end{align*}

11083

640

\begin{align*} 2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y&=0 \\ \end{align*}

11084

641

\begin{align*} 2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y&=0 \\ \end{align*}

11085

642

\begin{align*} t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y&=0 \\ \end{align*}

11086

643

\begin{align*} t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y&=0 \\ \end{align*}

11087

644

\begin{align*} t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y&=0 \\ \end{align*}

11088

645

\begin{align*} t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y&=0 \\ \end{align*}

11089

646

\begin{align*} t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y&=0 \\ \end{align*}

11090

647

\begin{align*} t y^{\prime \prime }+t y^{\prime }+2 y&=0 \\ \end{align*}

11091

648

\begin{align*} t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y&=0 \\ \end{align*}

11092

649

\begin{align*} t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y&=0 \\ \end{align*}

11093

650

\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}

11094

651

\begin{align*} \left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+y&=0 \\ \end{align*}

11095

652

\begin{align*} 4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \\ \end{align*}

11096

653

\begin{align*} f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\ \end{align*}

11097

654

\begin{align*} z y^{\prime \prime }-2 y^{\prime }+y z&=0 \\ \end{align*}

11098

655

\begin{align*} z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}&=0 \\ \end{align*}

11099

656

\begin{align*} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y&=0 \\ \end{align*}

11100

657

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}

11101

658

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}

11102

659

\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-1\right ) y&=0 \\ \end{align*}

11103

660

\begin{align*} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y&=0 \\ \end{align*}

11104

661

\begin{align*} y^{\prime \prime }+2 y^{\prime } x +4 y&=0 \\ \end{align*}

11105

662

\begin{align*} y^{\prime \prime }+y^{\prime } x +3 y&=0 \\ \end{align*}

11106

663

\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*}

11107

664

\begin{align*} \left (-4 x^{2}+1\right ) y^{\prime \prime }-20 y^{\prime } x -16 y&=0 \\ \end{align*}

11108

665

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\ \end{align*}

11109

666

\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (x +2\right ) y&=0 \\ \end{align*}

11110

667

\begin{align*} \left (2 x^{2}+1\right ) y^{\prime \prime }+7 y^{\prime } x +2 y&=0 \\ \end{align*}

11111

668

\begin{align*} 4 y^{\prime \prime }+y^{\prime } x +4 y&=0 \\ \end{align*}

11112

669

\begin{align*} y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}

11113

670

\begin{align*} 4 x y^{\prime \prime }-y^{\prime } x +2 y&=0 \\ \end{align*}

11114

671

\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\ \end{align*}

11115

672

\begin{align*} 3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y&=0 \\ \end{align*}

11116

673

\begin{align*} 2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y&=0 \\ \end{align*}

11117

674

\begin{align*} 4 x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align*}

11118

675

\begin{align*} x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \\ \end{align*}

11119

676

\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\ \end{align*}

11120

677

\begin{align*} x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y&=0 \\ \end{align*}

11121

678

\begin{align*} x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \\ \end{align*}

11122

679

\begin{align*} x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y&=0 \\ \end{align*}

11123

680

\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\left (x +2\right ) y&=0 \\ \end{align*}

11124

681

\begin{align*} x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y&=0 \\ \end{align*}

11125

682

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }+x^{2} y^{\prime }-2 y&=0 \\ \end{align*}

11126

683

\begin{align*} x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y&=0 \\ \end{align*}

11127

684

\begin{align*} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-y&=0 \\ \end{align*}

11128

685

\begin{align*} x^{2} y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+4 y&=0 \\ \end{align*}

11129

686

\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-2 y&=0 \\ \end{align*}

11130

687

\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }-\left (3 x +2\right ) y&=0 \\ \end{align*}

11131

688

\begin{align*} x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y&=0 \\ \end{align*}

11132

689

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y&=0 \\ \end{align*}

11133

690

\begin{align*} x^{2} y^{\prime \prime }+2 x \left (x +2\right ) y^{\prime }+2 \left (1+x \right ) y&=0 \\ \end{align*}

11134

691

\begin{align*} x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+\left (1-x \right ) y&=0 \\ \end{align*}

11135

692

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x \left (2 x +1\right ) y^{\prime }+\left (4 x -1\right ) y&=0 \\ \end{align*}

11136

693

\begin{align*} x^{2} y^{\prime \prime }+x \left (x +4\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}

11137

694

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {9}{4}\right ) y&=0 \\ \end{align*}

11138

695

\begin{align*} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*}

11139

696

\begin{align*} 2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y&=0 \\ \end{align*}

11140

697

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

11141

698

\begin{align*} x y^{\prime \prime }+\left (x +n \right ) y^{\prime }+\left (n +1\right ) y&=0 \\ \end{align*}

11142

699

\begin{align*} x^{4} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*}

11143

700

\begin{align*} x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y&=0 \\ \end{align*}

11144

701

\begin{align*} \left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \\ \end{align*}

11145

702

\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}

11146

703

\begin{align*} x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}

11147

704

\begin{align*} x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (-\frac {1}{4} x -x^{2}\right ) y^{\prime }-\frac {5 y x}{16}&=0 \\ \end{align*}

11148

705

\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \\ \end{align*}

11149

706

\begin{align*} x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\ \end{align*}

11150

707

\begin{align*} x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y&=0 \\ \end{align*}

11151

708

\begin{align*} 2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}&=0 \\ \end{align*}

11152

709

\begin{align*} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4}&=0 \\ \end{align*}

11153

710

\begin{align*} 2 x \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}

11154

711

\begin{align*} 2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y&=0 \\ \end{align*}

11155

712

\begin{align*} x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9}&=0 \\ \end{align*}

11156

713

\begin{align*} 4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}&=0 \\ \end{align*}

11157

714

\begin{align*} u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}

11158

715

\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}

11159

716

\begin{align*} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}

11160

717

\begin{align*} u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u&=0 \\ \end{align*}

11161

718

\begin{align*} u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \\ \end{align*}

11162

719

\begin{align*} -a^{2} y+y^{\prime \prime }&=\frac {6 y}{x^{2}} \\ \end{align*}

11163

720

\begin{align*} y^{\prime \prime }+n^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}

11164

721

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\frac {1}{4}\right ) y&=0 \\ \end{align*}

11165

722

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}}&=0 \\ \end{align*}

11166

723

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {25}{4}\right ) y&=0 \\ \end{align*}

11167

724

\begin{align*} y^{\prime \prime }+q y^{\prime }&=\frac {2 y}{x^{2}} \\ \end{align*}

11168

725

\begin{align*} x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}

11169

726

\begin{align*} \left (-x +2\right ) x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ \end{align*}

11170

727

\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

11171

728

\begin{align*} x y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}

11172

729

\begin{align*} 3 x y^{\prime \prime }-2 \left (3 x -1\right ) y^{\prime }+\left (3 x -2\right ) y&=0 \\ \end{align*}

11173

730

\begin{align*} x \left (1+x \right ) y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+y&=0 \\ \end{align*}

11174

731

\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}

11175

732

\begin{align*} \left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}

11176

733

\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

11177

734

\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

11178

735

\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\ \end{align*}

11179

736

\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\ \end{align*}

11180

737

\begin{align*} \left (2 x -3\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}

11181

738

\begin{align*} y^{\prime \prime }-y^{\prime } x -3 y&=0 \\ \end{align*}

11182

739

\begin{align*} y-y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

11183

740

\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}

11184

741

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y&=0 \\ \end{align*}

11185

742

\begin{align*} x \left (1+x \right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (-1+x \right ) y&=0 \\ \end{align*}

11186

743

\begin{align*} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}

11187

744

\begin{align*} x y^{\prime \prime }+y^{\prime } x -2 y&=0 \\ \end{align*}

11188

745

\begin{align*} x \left (-1+x \right )^{2} y^{\prime \prime }-2 y&=0 \\ \end{align*}

11189

746

\begin{align*} y^{\prime \prime }-2 y^{\prime } x +x^{2} y&=0 \\ \end{align*}

11190

747

\begin{align*} x \left (-x^{2}+2\right ) y^{\prime \prime }-\left (x^{2}+4 x +2\right ) \left (\left (1-x \right ) y^{\prime }+y\right )&=0 \\ \end{align*}

11191

748

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }-\left (2 x +1\right ) \left (-y+y^{\prime } x \right )&=0 \\ \end{align*}

11192

749

\begin{align*} \left (-x +3\right ) y-x \left (4-x \right ) y^{\prime }+2 \left (-x +2\right ) x^{2} y^{\prime \prime }&=0 \\ \end{align*}

11193

750

\begin{align*} x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \\ \end{align*}

11194

751

\begin{align*} 4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}

11195

754

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0 \\ \end{align*}

11196

755

\begin{align*} x \left (x +2\right ) y^{\prime \prime }+2 \left (1+x \right ) y^{\prime }-2 y&=0 \\ \end{align*}

11197

757

\begin{align*} x \left (x +2\right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }-4 y&=0 \\ \end{align*}

11198

758

\begin{align*} \left (-1+x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}

11199

759

\begin{align*} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

11200

760

\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}

11201

761

\begin{align*} \left (x^{2}-2 x +10\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*}

11202

762

\begin{align*} 2 y-y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*}

11203

763

\begin{align*} \left (x +2\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}

11204

764

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-6 y&=0 \\ \end{align*}

11205

765

\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y&=0 \\ \end{align*}

11206

766

\begin{align*} \left (-1+x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}

11207

769

\begin{align*} x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}&=0 \\ \end{align*}

11208

770

\begin{align*} 2 x y^{\prime \prime }-y^{\prime }+2 y&=0 \\ \end{align*}

11209

771

\begin{align*} 2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y&=0 \\ \end{align*}

11210

772

\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y&=0 \\ \end{align*}

11211

773

\begin{align*} x y^{\prime \prime }+2 y^{\prime }-y x&=0 \\ \end{align*}

11212

774

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

11213

775

\begin{align*} x y^{\prime \prime }+\left (-6+x \right ) y^{\prime }-3 y&=0 \\ \end{align*}

11214

776

\begin{align*} x^{4} y^{\prime \prime }+\lambda y&=0 \\ \end{align*}

11215

777

\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\ \end{align*}

11216

778

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

11217

779

\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \\ \end{align*}

11218

780

\begin{align*} x y^{\prime \prime }+3 y^{\prime }+x^{3} y&=0 \\ \end{align*}

11219

781

\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}

11220

782

\begin{align*} 16 x^{2} y^{\prime \prime }+32 y^{\prime } x +\left (x^{4}-12\right ) y&=0 \\ \end{align*}

11221

783

\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

11222

784

\begin{align*} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y&=0 \\ \end{align*}

11223

785

\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\ \end{align*}

11224

786

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\ \end{align*}

11225

787

\begin{align*} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y&=0 \\ \end{align*}

11226

788

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y&=0 \\ \end{align*}

11227

789

\begin{align*} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*}

11228

790

\begin{align*} x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align*}

11229

791

\begin{align*} 2 x \left (-1+x \right ) y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y&=0 \\ \end{align*}

11230

792

\begin{align*} x y^{\prime \prime }+2 y^{\prime }+4 y x&=0 \\ \end{align*}

11231

793

\begin{align*} x y^{\prime \prime }+\left (-2 x +2\right ) y^{\prime }+\left (x -2\right ) y&=0 \\ \end{align*}

11232

794

\begin{align*} x^{2} y^{\prime \prime }+6 y^{\prime } x +\left (4 x^{2}+6\right ) y&=0 \\ \end{align*}

11233

795

\begin{align*} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y&=0 \\ \end{align*}

11234

796

\begin{align*} x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align*}

11235

797

\begin{align*} 4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y&=0 \\ \end{align*}

11236

798

\begin{align*} 2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y&=0 \\ \end{align*}

11237

799

\begin{align*} 3 t \left (t +1\right ) y^{\prime \prime }+t y^{\prime }-y&=0 \\ \end{align*}

11238

800

\begin{align*} x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4}&=0 \\ \end{align*}

11239

801

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (x^{2}-1\right ) y}{4}&=0 \\ \end{align*}

11240

802

\begin{align*} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (-1+x \right ) y&=0 \\ \end{align*}

11241

803

\begin{align*} y-\left (1+x \right ) y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}

11242

804

\begin{align*} x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y&=0 \\ \end{align*}

11243

805

\begin{align*} x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y&=0 \\ \end{align*}

11244

806

\begin{align*} 2 x y^{\prime \prime }+\left (x -2\right ) y^{\prime }-y&=0 \\ \end{align*}

11245

807

\begin{align*} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*}

11246

808

\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \\ \end{align*}

11247

809

\begin{align*} u^{\prime \prime }+2 u^{\prime }+u&=0 \\ \end{align*}

11248

810

\begin{align*} u^{\prime \prime }-\left (2 x +1\right ) u^{\prime }+\left (x^{2}+x -1\right ) u&=0 \\ \end{align*}

11249

811

\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \\ \end{align*}

11250

812

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}

11251

813

\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (1+x \right )^{2}}&=0 \\ \end{align*}

11252

815

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

11253

816

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

11254

817

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

11255

818

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

11256

819

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

11257

820

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

11258

821

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

11259

822

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

11260

823

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

11261

824

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

11262

825

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x&=0 \\ \end{align*}

11263

826

\begin{align*} x y^{\prime \prime }+2 y^{\prime }+y x&=0 \\ \end{align*}

11264

827

\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y x&=0 \\ \end{align*}

11265

828

\begin{align*} x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y&=0 \\ \end{align*}

11266

829

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}

11267

830

\begin{align*} x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+2 y&=0 \\ \end{align*}

11268

831

\begin{align*} x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y&=0 \\ \end{align*}

11269

832

\begin{align*} 2 x^{2} \left (x +2\right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (1+x \right ) y&=0 \\ \end{align*}

11270

833

\begin{align*} x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}

11271

834

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

11272

835

\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -\left (x^{2}+\frac {5}{4}\right ) y&=0 \\ \end{align*}

11273

836

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

11274

837

\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y&=0 \\ \end{align*}

11275

838

\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}

11276

839

\begin{align*} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\ \end{align*}

11277

840

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

11278

841

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (-8 x^{2}+4 x \right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y&=0 \\ \end{align*}

11279

843

\begin{align*} y^{\prime \prime }&=0 \\ \end{align*}

11280

844

\begin{align*} y^{\prime \prime }&=\frac {2 y}{x^{2}} \\ \end{align*}

11281

845

\begin{align*} y^{\prime \prime }&=\frac {6 y}{x^{2}} \\ \end{align*}

1.2 section 2. Solution found using all possible Kovacic cases

Table 1.3: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

11282

1

\begin{align*} y^{\prime \prime }&=\left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (-1+x \right )^{2}}+\frac {3}{16 x \left (-1+x \right )}\right ) y \\ \end{align*}

11283

2

\begin{align*} y^{\prime \prime }&=\frac {20 y}{x^{2}} \\ \end{align*}

11284

3

\begin{align*} y^{\prime \prime }&=\frac {12 y}{x^{2}} \\ \end{align*}

11285

4

\begin{align*} y^{\prime \prime }-\frac {y}{4 x^{2}}&=0 \\ \end{align*}

11286

5

\begin{align*} x y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+\left (x +2\right ) y&=0 \\ \end{align*}

11287

6

\begin{align*} y^{\prime \prime }+\frac {y}{x^{2}}&=0 \\ \end{align*}

11288

7

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}

11289

8

\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}

11290

9

\begin{align*} x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y&=0 \\ \end{align*}

Table 1.5: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

11291

Kovacic 1985 paper. page 13. section 3.2, example 1

\begin{align*} y^{\prime \prime }&=\frac {\left (4 x^{6}-8 x^{5}+12 x^{4}+4 x^{3}+7 x^{2}-20 x +4\right ) y}{4 x^{4}} \\ \end{align*}

11292

Kovacic 1985 paper. page 14. section 3.2, example 2

\begin{align*} y^{\prime \prime }&=\left (\frac {6}{x^{2}}-1\right ) y \\ \end{align*}

11293

Kovacic 1985 paper. page 15. Weber equation

\begin{align*} y^{\prime \prime }&=\left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y \\ \end{align*}

11294

Kovacic 1985 paper. page 19. section 4.2. Example 1

\begin{align*} y^{\prime \prime }&=\left (\frac {1}{x}-\frac {3}{16 x^{2}}\right ) y \\ \end{align*}

11295

Kovacic 1985 paper. page 23. section 5.2. Example 1

\begin{align*} y^{\prime \prime }&=\left (-\frac {3}{16 x^{2}}-\frac {2}{9 \left (-1+x \right )^{2}}+\frac {3}{16 x \left (-1+x \right )}\right ) y \\ \end{align*}

11296

Kovacic 1985 paper. page 25. section 5.2. Example 2

\begin{align*} y^{\prime \prime }&=-\frac {\left (5 x^{2}+27\right ) y}{36 \left (x^{2}-1\right )^{2}} \\ \end{align*}

11297

Kovacic 2005 paper. Example 2

\begin{align*} y^{\prime \prime }&=-\frac {y}{4 x^{2}} \\ \end{align*}

11298

David Saunders 1981 paper. Example 1

\begin{align*} y^{\prime \prime }&=\left (x^{2}+3\right ) y \\ \end{align*}

11299

David Saunders 1981 paper. Example 3

\begin{align*} x^{2} y^{\prime \prime }&=2 y \\ \end{align*}

11300

Carolyn J. Smith 1984 paper. Appendix B examples and tests. Example 1

\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}

11301

Carolyn J. Smith 1984 paper. Appendix B examples and tests. Example 2

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}

11302

Carolyn J. Smith 1984 paper. Appendix B examples and tests. Example 3

\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }-3 y&=0 \\ \end{align*}