2.3.1 Problems 1 to 100

Table 2.585: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

1

26125

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

0.016

2

4536

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

0.018

3

10381

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

0.018

4

13080

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

0.018

5

27848

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

0.018

6

27859

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \sqrt {x^{2}+9}\\ y \left (-4\right )&=0\\ \end {array} \]

0.018

7

604

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {10}{x^{2}+1}\\ y \left (0\right )&=0\\ \end {array} \]

0.019

8

3832

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

0.019

9

20991

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

0.019

10

21001

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

0.019

11

27849

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=50\\ x \left (0\right )&=20\\ x^{\prime }\left (0\right )&=10\\ \end {array} \]

0.019

12

27866

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=-20\\ x \left (0\right )&=5\\ x^{\prime }\left (0\right )&=-15\\ \end {array} \]

0.019

13

3831

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=3 t\\ x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=5\\ \end {array} \]

0.020

14

3890

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=2 t +1\\ x \left (0\right )&=4\\ x^{\prime }\left (0\right )&=-7\\ \end {array} \]

0.020

15

4549

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

0.020

16

22885

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

0.020

17

26137

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

0.020

18

27861

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=50 \sin \left (5 t \right )\\ x \left (0\right )&=8\\ x^{\prime }\left (0\right )&=-10\\ \end {array} \]

0.020

19

27863

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

0.020

20

27865

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

0.020

21

4535

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

0.021

22

4572

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

0.021

23

18634

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

0.021

24

20676

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

0.021

25

20992

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

0.021

26

26127

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

0.021

27

27855

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

0.021

28

27857

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

0.021

29

27858

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

0.021

30

27928

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

0.021

31

27964

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

0.021

32

27862

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

0.022

33

27864

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

0.022

34

27927

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

0.022

35

4573

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

0.023

36

6582

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

0.023

37

8198

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

0.023

38

13079

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

0.023

39

13082

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

0.023

40

19211

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

0.023

41

26135

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

0.023

42

26136

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

0.023

43

26749

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

0.023

44

27771

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

0.023

45

27814

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

0.023

46

27816

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

0.023

47

27854

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=64^{{1}/{3}} \left (y x \right )^{{1}/{3}} \end {array} \]

0.023

48

27860

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

0.023

49

27929

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

0.023

50

27930

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

0.023

51

27931

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

0.023

52

3823

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

0.024

53

3891

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

0.024

54

13077

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {1+\sqrt {x}}{1+\sqrt {y}} \end {array} \]

0.024

55

13081

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

0.024

56

20810

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

0.024

57

21238

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

0.024

58

27198

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

0.024

59

27815

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

0.024

60

27856

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

0.024

61

13123

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

0.025

62

17824

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

0.025

63

18631

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

0.025

64

13078

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

0.026

65

18714

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

0.026

66

21235

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

0.026

67

24092

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

0.026

68

26138

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

0.026

69

26139

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

0.026

70

27821

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

0.026

71

2815

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

0.027

72

6608

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

0.027

73

8092

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

0.027

74

18705

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

0.027

75

18708

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

0.027

76

21236

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

0.027

77

21237

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

0.027

78

22893

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +5 y&=7 x^{2}\\ y \left (2\right )&=5\\ \end {array} \]

0.027

79

24089

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime } x +y&=10 \sqrt {x} \end {array} \]

0.027

80

25360

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+3 y^{\prime } x&=12 x \end {array} \]

0.027

81

18407

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

0.028

82

18422

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime } x -3 y&=9 x^{3} \end {array} \]

0.028

83

18423

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

0.028

84

18711

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

0.028

85

18715

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

0.028

86

19212

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -3 y&=x^{3}\\ y \left (1\right )&=10\\ \end {array} \]

0.028

87

25389

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

0.028

88

25392

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

0.028

89

608

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

0.029

90

2792

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

0.029

91

8091

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

0.029

92

18405

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

0.029

93

18417

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

0.029

94

18421

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

0.029

95

18707

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

0.029

96

18717

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

0.029

97

19061

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime }+3 x^{3} y&=6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}}\\ y \left (0\right )&=1\\ \end {array} \]

0.029

98

19062

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

0.029

99

20209

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {x+y \,{\mathrm e}^{y}}{x^{\prime }}&=1 \end {array} \]

0.029

100

22886

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

0.029