Chapter 1
Lookup tables for all problems in current book

1.1 section 1.0
1.2 section 2.0
1.3 section 3.0
1.4 section 4.0
1.5 section 5.0

1.1 section 1.0

Table 1.1: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

9987

1

\begin{align*} y^{\prime }&=\frac {\cos \left (y\right ) \sec \left (x \right )}{x} \\ \end{align*}

9988

2

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

9989

3

\begin{align*} y^{\prime }&=\frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x} \\ \end{align*}

9990

4

\begin{align*} y^{\prime }&=\left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right ) \\ \end{align*}

9991

5

\begin{align*} y^{\prime }&=1+y \\ \end{align*}

9992

6

\begin{align*} y^{\prime }&=1+x \\ \end{align*}

9993

7

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

9994

8

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

9995

9

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

9996

10

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

9997

11

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

9998

12

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

9999

13

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

10000

14

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

10001

15

\begin{align*} y^{\prime }&=\frac {1}{x} \\ \end{align*}

10002

16

\begin{align*} y^{\prime }&=\frac {-y x -1}{4 x^{3} y-2 x^{2}} \\ \end{align*}

10003

17

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

10004

18

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

10005

19

\begin{align*} y^{\prime }&=\sqrt {1-x^{2}-y^{2}} \\ \end{align*}

10006

20

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

10007

21

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

10008

23

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

10009

24

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

10010

25

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

10011

26

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

10012

27

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

10013

28

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

10014

29

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

10015

30

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

10016

31

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

10017

32

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

10018

33

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

10019

34

\begin{align*} p^{\prime }&=a p-b p^{2} \\ p \left (\operatorname {t0} \right ) &= \operatorname {p0} \\ \end{align*}

10020

35

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

10021

36

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

10022

37

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

10023

38

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

10024

39

\begin{align*} u^{\prime }+u^{2}&=\frac {1}{x^{{4}/{5}}} \\ \end{align*}

10025

40

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

10026

41

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

10027

41

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

10028

42

\begin{align*} y^{\prime \prime }+y^{\prime }+4 y&=1 \\ \end{align*}

10029

43

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

10030

44

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

10031

45

\begin{align*} y^{\prime } y&=1-x {y^{\prime }}^{3} \\ \end{align*}

10032

46

\begin{align*} f^{\prime }&=\frac {1}{f} \\ \end{align*}

10033

47

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

10034

48

\begin{align*} \left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime }&=0 \\ y \left (3\right ) &= 2 \pi \\ y^{\prime }\left (3\right ) &= {\frac {2}{3}} \\ \end{align*}

10035

49

\begin{align*} t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y&=0 \\ \end{align*}

10036

50

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

10037

51

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

10038

52

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

10039

53

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

10040

54

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

10041

55

\begin{align*} y^{\prime \prime }&=1 \\ \end{align*}

10042

56

\begin{align*} y^{\prime \prime }&=f \left (t \right ) \\ \end{align*}

10043

57

\begin{align*} y^{\prime \prime }&=k \\ \end{align*}

10044

58

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

10045

59

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

10046

60

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

10047

61

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

10048

62

\begin{align*} y y^{\prime \prime }&=1 \\ \end{align*}

10049

63

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

10050

64

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

10051

65

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

10052

66

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

10053

67

\begin{align*} 3 y y^{\prime \prime }+y&=5 \\ \end{align*}

10054

68

\begin{align*} a y y^{\prime \prime }+b y&=c \\ \end{align*}

10055

69

\begin{align*} a y^{2} y^{\prime \prime }+b y^{2}&=c \\ \end{align*}

10056

70

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

10057

71

\begin{align*} x^{\prime }\left (t \right )&=9 x \left (t \right )+4 y \left (t \right ) \\ y^{\prime }\left (t \right )&=-6 x \left (t \right )-y \left (t \right ) \\ z^{\prime }\left (t \right )&=6 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right ) \\ \end{align*}

10058

72

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

10059

73

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

10060

74

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

10061

75

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

10062

76

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

10063

77

\begin{align*} x^{\prime }&=4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x \\ \end{align*}

10064

78

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

10065

78

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

10066

79

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

10067

80

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

10068

81

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

10069

82

\begin{align*} z^{\prime \prime }+3 z^{\prime }+2 z&=24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \\ \end{align*}

10070

83

\begin{align*} y^{\prime }&=\sqrt {1-y^{2}} \\ \end{align*}

10071

84

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

10072

85

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

10073

86

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

10074

87

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

10075

88

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

10076

88

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

10077

89

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

10078

90

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

1.2 section 2.0

Table 1.3: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

10079

1

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

10080

2

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

10081

3

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

10082

4

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

10083

5

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

10084

6

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

10085

7

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x -x^{5}+24&=0 \\ \end{align*}

10086

8

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

10087

9

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

10088

10

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

10089

11

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

10090

12

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

10091

13

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

10092

14

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

10093

15

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

10094

16

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

10095

16

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

10096

17

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

10097

18

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

10098

19

\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x^{3}+1&=0 \\ \end{align*}

10099

20

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

10100

21

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

10101

22

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

10102

23

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

10103

24

\begin{align*} y^{\prime \prime }-6 y^{\prime }-y x -x^{3}+2&=0 \\ \end{align*}

10104

25

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

10105

26

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

10106

27

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

10107

28

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

10108

29

\begin{align*} y^{\prime \prime }-y x -x^{6}+64&=0 \\ \end{align*}

10109

30

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

10110

31

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

10111

32

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

10112

33

\begin{align*} y^{\prime \prime }-y x -x^{6}-x^{3}+42&=0 \\ \end{align*}

10113

34

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

10114

35

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

10115

36

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

10116

37

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

10117

38

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

10118

39

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

10119

40

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

10120

41

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

10121

42

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

10122

43

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

10123

44

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

10124

45

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

10125

46

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

10126

47

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

10127

48

\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x}&=0 \\ \end{align*}

10128

49

\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x}&=0 \\ \end{align*}

10129

50

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

10130

51

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

10131

52

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

10132

50

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

1.3 section 3.0

Table 1.5: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

10133

1

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

10134

2

\begin{align*} w^{\prime }&=-\frac {1}{2}-\frac {\sqrt {1-12 w}}{2} \\ w \left (1\right ) &= -1 \\ \end{align*}

10135

3

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

10136

4

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

10137

5

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

10138

6

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

10139

7

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

10140

8

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

10141

9

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

10142

10

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

10143

11

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

10144

12

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

10145

13

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

10146

14

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

10147

15

\begin{align*} x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y&=1 \\ \end{align*}

10148

16

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

10149

17

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

10150

18

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

10151

19

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

10152

20

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

10153

21

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

10154

22

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

10155

23

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

10156

24

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

10157

25

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

10158

26

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

10159

27

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

10160

28

\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {y}{x}} \\ \end{align*}

10161

29

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

10162

30

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

10163

31

\begin{align*} v v^{\prime }&=\frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \\ \end{align*}

1.4 section 4.0

Table 1.7: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

10164

1

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

10165

2

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

10166

3

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

10167

4

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

10168

5

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

10169

6

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

10170

7

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

10171

8

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

10172

9

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

10173

10

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

10174

11

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

10175

12

\begin{align*} 2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\cos \left (x \right )+\sin \left (x \right ) \\ \end{align*}
Series expansion around \(x=0\).

10176

13

\begin{align*} x^{2} y^{\prime \prime }+\left (\cos \left (x \right )-1\right ) y^{\prime }+{\mathrm e}^{x} y&=0 \\ \end{align*}
Series expansion around \(x=0\).

10177

14

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

10178

15

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

10179

16

\begin{align*} \left (1+x \right ) \left (3 x -1\right ) y^{\prime \prime }+\cos \left (x \right ) y^{\prime }-3 y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

10180

17

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

10181

18

\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y x&=x^{2}+2 x \\ \end{align*}
Series expansion around \(x=0\).

10182

19

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

10183

20

\begin{align*} 2 x^{2} y^{\prime \prime }+2 y^{\prime } x -y x&=1 \\ \end{align*}
Series expansion around \(x=0\).

10184

21

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

10185

22

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

10186

23

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

10187

24

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

10188

24

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

10189

24

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

10190

24

\begin{align*} 2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=x^{3} \cos \left (x \right )+\sin \left (x \right )^{2} \\ \end{align*}
Series expansion around \(x=0\).

10191

24

\begin{align*} 2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (-x^{2}+1\right ) y&=\ln \left (x \right ) \\ \end{align*}
Series expansion around \(x=1\).

10192

25

\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*}
Series expansion around \(x=0\).

10193

26

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

10194

27

\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*}
Series expansion around \(x=0\).

10195

28

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

10196

29

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

10197

31

\begin{align*} x^{2} y^{\prime \prime }+y&=0 \\ \end{align*}
Series expansion around \(x=0\).

10198

32

\begin{align*} -y+y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}
Series expansion around \(x=0\).

10199

33

\begin{align*} 4 x y^{\prime \prime }+2 y^{\prime }+y&=0 \\ \end{align*}
Series expansion around \(x=0\).

10200

34

\begin{align*} -y+y^{\prime }+x y^{\prime \prime }&=0 \\ \end{align*}
Series expansion around \(x=0\).

10201

35

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

10202

36

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

10203

37

\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*}
Series expansion around \(x=0\).

10204

38

\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*}
Series expansion around \(x=0\).

10205

39

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

10206

40

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

10207

41

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

10208

42

\begin{align*} 2 x^{2} y^{\prime \prime }+2 y^{\prime } x -y x&=\cos \left (x \right ) \sin \left (x \right ) \\ \end{align*}
Series expansion around \(x=0\).

10209

43

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

10210

44

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

10211

45

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

10212

46

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

10213

47

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

10214

48

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

10215

49

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

10216

50

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

10217

51

\begin{align*} x^{2} y^{\prime \prime }-9 y^{\prime } x +25 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

10218

52

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

10219

53

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

10220

54

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

10221

55

\begin{align*} 2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=0 \\ \end{align*}
Series expansion around \(x=0\).

10222

56

\begin{align*} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

10223

57

\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +4 x^{4} y&=0 \\ \end{align*}
Series expansion around \(x=0\).

10224

58

\begin{align*} x^{2} y^{\prime \prime }-y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

10225

59

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime }+y&=x \,{\mathrm e}^{x} \\ \end{align*}
Series expansion around \(x=0\).

10226

60

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

10227

61

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

10228

62

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

10229

63

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

10230

64

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

10231

65

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

10232

66

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

10233

67

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

10234

68

\begin{align*} y^{\prime \prime }+20 y^{\prime }+500 y&=100000 \cos \left (100 x \right ) \\ \end{align*}

10235

69

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

1.5 section 5.0

Table 1.9: Lookup table

ID

problem

ODE

Solved?

Maple

Mma

Sympy

10236

1

\begin{align*} y^{\prime \prime }&=A y^{{2}/{3}} \\ \end{align*}

10237

2

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

10238

3

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

10239

4

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

10240

5

\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&=4 \sqrt {x}\, {\mathrm e}^{x} \\ \end{align*}

10241

6

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

10242

7

\begin{align*} y^{\prime }+y&=\frac {1}{x} \\ \end{align*}
Series expansion around \(x=0\).

10243

8

\begin{align*} y^{\prime }+y&=\frac {1}{x^{2}} \\ \end{align*}
Series expansion around \(x=0\).

10244

9

\begin{align*} y^{\prime } x +y&=0 \\ \end{align*}
Series expansion around \(x=0\).

10245

10

\begin{align*} y^{\prime }&=\frac {1}{x} \\ \end{align*}
Series expansion around \(x=0\).

10246

11

\begin{align*} y^{\prime \prime }&=\frac {1}{x} \\ \end{align*}
Series expansion around \(x=0\).

10247

12

\begin{align*} y^{\prime \prime }+y^{\prime }&=\frac {1}{x} \\ \end{align*}
Series expansion around \(x=0\).

10248

13

\begin{align*} y^{\prime \prime }+y&=\frac {1}{x} \\ \end{align*}
Series expansion around \(x=0\).

10249

14

\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\frac {1}{x} \\ \end{align*}
Series expansion around \(x=0\).

10250

15

\begin{align*} h^{2}+\frac {2 a h}{\sqrt {1+{h^{\prime }}^{2}}}&=b^{2} \\ \end{align*}

10251

16

\begin{align*} y^{\prime \prime }+2 y^{\prime }-24 y&=16-\left (x +2\right ) {\mathrm e}^{4 x} \\ \end{align*}

10252

17

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -2} \\ y \left (1\right ) &= 4 \\ y^{\prime }\left (1\right ) &= 5 \\ \end{align*}
Using Laplace transform method.

10253

18

\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{a \cos \left (x \right )} \\ \end{align*}
Series expansion around \(x=0\).

10254

19

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

10255

20

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

10256

21

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

10257

22

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

10258

23

\begin{align*} y^{\prime }&=\frac {y x +3 x -2 y+6}{y x -3 x -2 y+6} \\ \end{align*}