1 Detailed lookup table and classification for each ODE

The following table 1 gives the classification of each ODE from Maple ODE advisor with a link to each ODE page as well. Clicking on the problem opens a new page that shows the result.

Table 1:ODE classification and performance for each differential equation
#

result

ODE 1

y′(x) = af(x)

[_quadrature]

Solution method Separable ODE, Dependent variable missing

Maple ✓
Mathematica ✓

ODE 2

y′(x) = y(x) + x + sin(x)

[[_linear, ‘class A‘]]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 3

y′(x) = x2 + 2y(x) + 3cosh(x)

[[_linear, ‘class A‘]]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 4

y′(x) = a + bx + cy(x)

[[_linear, ‘class A‘]]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 5

y′(x) = acos(bx + c) + ky(x)

[[_linear, ‘class A‘]]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 6

y′(x) = asin(bx + c) + ky(x)

[[_linear, ‘class A‘]]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 7

y′(x) = a + bekx + cy(x)

[[_linear, ‘class A‘]]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 8

y′(x) = x( 2 ) x − y (x )

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 9

y′(x) = x( ) ay(x) + e−x2

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 10

y′(x) = x2( ) ax3 + by(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 11

y′(x) = axny(x)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 12

y′(x) = y(x)cos(x) + sin(x)cos(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 13

y′(x) = y(x)cos(x) + esin(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 14

y′(x) = y(x)cot(x)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 15

y′(x) = 1 − y(x)cot(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 16

y′(x) = xcsc(x) − y(x)cot(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 17

y′(x) = y(x)(cot(x) + 2csc(2x))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 18

y′(x) = sec(x) − y(x)cot(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 19

y′(x) = y(x)cot(x) + ex sin(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 20

y′(x) + 2y(x)cot(x) + csc(x) = 0

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 21

y′(x) = 4xcsc(x)sec2(x) − 2y(x)cot(2x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 22

y′(x) = 2

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 23

y′(x) = 4xcsc(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 24

y′(x) = 4xcsc(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 25

y′(x) = y(x)sec(x)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 26

y′(x) + tan(x) = (1 − y(x))sec(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 27

y′(x) = y(x)tan(x)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 28

y′(x) = y(x)tan(x) + cos(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 29

y′(x) = cos(x) − y(x)tan(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 30

y′(x) = sec(x) − y(x)tan(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 31

y′(x) = y(x)tan(x) + sin(2x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 32

y′(x) = sin(2x) − y(x)tan(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 33

y′(x) = 2y(x)tan(x) + sin(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 34

y′(x) = 2(y(x)tan(2x) + sec(2x) + 1)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 35

y′(x) = 3y(x)tan(x) + csc(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 36

y′(x) = y(x)(a + sin(log(x)) + cos(log(x)))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 37

y′(x) = 6e2x − y(x)tanh(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 38

y′(x) = y(x)f′(x) + f(x)f′(x)

odeadvisor timed out

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 39

y′(x) = f(x) + g(x)y(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 40

y′(x) = x2 − y(x)2

[_Riccati]

Solution method Series solution to y′(x) = f(x,y(x)), case f(x,y) analytic

Maple ✓
Mathematica ✓

ODE 41

f(x)2 + y′(x) = f′(x) + y(x)2

odeadvisor timed out

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✗

ODE 42

y′(x) − x + 1 = y(x)(y(x) + x)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 43

y′(x) = (y(x) + x)2

[[_homogeneous, ‘class C‘], _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 44

y′(x) = (x − y(x))2

[[_homogeneous, ‘class C‘], _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 45

y′(x) = (x − y(x))2 + 3(y(x) − x + 1)

[[_homogeneous, ‘class C‘], _Riccati]

Solution method Equation linear in the variables, y′(x) = f(a + bx + cy(x))

Maple ✓
Mathematica ✓

ODE 46

y′(x) = −y(x) + y(x)2 + 2x

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 47

y′(x) = x−y(x)

[[_1st_order, _with_linear_symmetries], _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 48

y′(x) = x + y(x) + 1

[[_1st_order, _with_linear_symmetries], _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 49

y′(x) = cos(x) − y(x)(sin(x) − y(x))

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 50

y′(x) = y(x)(y(x) + sin(2x)) + cos(2x)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 51

y′(x) = xf(x)y(x) + f(x) + y(x)2

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 52

y′(x) = (−4y(x) + x + 3)2

[[_homogeneous, ‘class C‘], _Riccati]

Solution method Equation linear in the variables, y′(x) = f(a + bx + cy(x))

Maple ✓
Mathematica ✓

ODE 53

y′(x) = (9y(x) + 4x + 1)2

[[_homogeneous, ‘class C‘], _Riccati]

Solution method Equation linear in the variables, y′(x) = f(a + bx + cy(x))

Maple ✓
Mathematica ✓

ODE 54

y′(x) = 3

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 55

y′(x) = a + by(x)2

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple ✓
Mathematica ✓

ODE 56

y′(x) = ax + by(x)2

[[_Riccati, _special]]

Solution method Riccati ODE, Main form

Maple ✓
Mathematica ✓

ODE 57

y′(x) = a + bx + cy(x)2

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 58

y′(x) = axn−1 + bx2n + cy(x)2

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 59

y′(x) = ax2 + by(x)2

[[_Riccati, _special]]

Solution method Riccati ODE, Main form

Maple ✓
Mathematica ✓

ODE 60

y′(x) = a0 + a1y(x) + a2y(x)2

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple ✓
Mathematica ✓

ODE 61

y′(x) = ay(x) + by(x)2 + f(x)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✗
Mathematica ✗

ODE 62

y′(x) = a(x − y(x))y(x) + 1

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 63

y′(x) = ay(x)2 + f(x) + g(x)y(x)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✗
Mathematica ✗

ODE 64

y′(x) = xy(x)(y(x) + 3)

[_separable]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 65

y′(x) = −x3 + y(x) − xy(x)2 − x + 1

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 66

y′(x) = x

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 67

y′(x) = − + (1 − 2x)y(x) + x

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 68

y′(x) = axy(x)2

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 69

y′(x) = xn

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 70

y′(x) = axm + bxny(x)2

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 71

y′(x) = y(x)(a + by(x)cos(kx))

[_Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 72

y′(x) = sin(x)

[_linear]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 73

y′(x) + 4csc(x) = y(x)2 sin(x) + y(x)(3 − cot(x))

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 74

y′(x) = y(x)sec(x) + (sin(x) − 1)2

[_linear]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 75

y′(x) + tan(x) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 76

y′(x) = f(x) + g(x)y(x) + h(x)y(x)2

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✗
Mathematica ✗

ODE 77

y′(x) = f(x)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 78

y(x)2(ax + y(x)) + y′(x)

[_Abel]

Solution method Abel ODE, First kind

Maple ✓
Mathematica ✗

ODE 79

y′(x) = y(x)2

[_Abel]

Solution method Abel ODE, First kind

Maple ✓
Mathematica ✓

ODE 80

3a(y(x) + 2x)y(x)2 + y′(x) = 0

[_Abel]

Solution method Abel ODE, First kind

Maple ✓
Mathematica ✓

ODE 81

y′(x) = y(x)

[_quadrature]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 82

y′(x) = a0 + a1y(x) + a2y(x)2 + a3y(x)3

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple ✓
Mathematica ✓

ODE 83

y′(x) = xy(x)3

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 84

y′(x) + y(x) = 0

[_Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 85

y′(x) = y(x)2(a + bxy(x))

[[_homogeneous, ‘class G‘], _Abel]

Solution method Abel ODE, First kind

Maple ✓
Mathematica ✓

ODE 86

y(x)3 + y′(x) + 3xy(x)2 = 0

[_Abel]

Solution method Abel ODE, First kind

Maple ✓
Mathematica ✓

ODE 87

y′(x) = y(x)2

[_Abel]

Solution method Abel ODE, First kind

Maple ✗
Mathematica ✗

ODE 88

2xy(x) + y′(x) = 0

[_Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 89

y′(x) = y(x)2 − axy(x)3

[_Abel]

Solution method Abel ODE, First kind

Maple ✗
Mathematica ✗

ODE 90

y′(x) = ay(x)2 + xy(x)3

[_Abel]

Solution method Abel ODE, First kind

Maple ✗
Mathematica ✗

ODE 91

y′(x) + y(x) = 0

[_Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 92

y′(x) + y(x)3 tan(x)sec(x) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 93

y′(x) = f0(x) + f1(x)y(x) + f2(x)y(x)2 + f3(x)y(x)3

[_Abel]

Solution method Abel ODE, First kind

Maple ✗
Mathematica ✗

ODE 94

y′(x) = y(x)

[_Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 95

y′(x) = ax + by(x)n

[[_homogeneous, ‘class G‘], _Chini]

Solution method Change of Variable, new dependent variable

Maple ✓
Mathematica ✓

ODE 96

y′(x) = f(x)y(x) + g(x)y(x)k

[_Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 97

y′(x) = f(x) + g(x)y(x) + h(x)y(x)n

[_Chini]

Solution method Change of Variable, new dependent variable

Maple ✗
Mathematica ✗

ODE 98

y′(x) = f(x)y(x)m + g(x)y(x)n

[NONE]

Solution method Change of Variable, new dependent variable

Maple ✗
Mathematica ✗

ODE 99

y′(x) =

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple ✓
Mathematica ✓

ODE 100

y′(x) = a + + by(x)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple ✓
Mathematica ✓

ODE 101

y′(x) = ax + b

[[_homogeneous, ‘class G‘], _Chini]

Solution method Change of Variable, new dependent variable

Maple ✓
Mathematica ✓

ODE 102

x3 + y′(x) = x

[[_1st_order, _with_linear_symmetries]]

Solution method Homogeneous equation, isobaric equation

Maple ✓
Mathematica ✓

ODE 103

y′(x) + 2y(x) = 0

[_Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 104

y′(x) =

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple ✓
Mathematica ✓

ODE 105

y′(x) = y(x)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple ✓
Mathematica ✓

ODE 106

g(x)(f(x) − y(x)) + y′(x) = 0

[‘y=_G(x,y’)‘]

Solution method Change of Variable, new dependent variable

Maple ✗
Mathematica ✗

ODE 107

y′(x) =

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 108

y′(x) = R1R2

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 109

y′(x) = cos2(x)cos(y(x))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 110

y′(x) = sec2(x)Cosy(y(x))cot(y(x))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 111

y′(x) = a + bcos(Ax + By(x))

[[_homogeneous, ‘class C‘], _dAlembert]

Solution method Change of Variable, new dependent variable

Maple ✓
Mathematica ✓

ODE 112

y′(x) = −cos(y(x)) + f′(x) − f(x)sin(y(x)) + 1

odeadvisor timed out

Solution method Change of Variable, new dependent variable

Maple ✓
Mathematica ✓

ODE 113

g(x)sin(ay(x)) + h(x)cos(ay(x)) + f(x) + y′(x) = 0

[‘y=_G(x,y’)‘]

Solution method Change of Variable, new dependent variable

Maple ✗
Mathematica ✗

ODE 114

y′(x) = a + bcos(y(x))

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple ✓
Mathematica ✓

ODE 115

x + y′(x) = 0

[‘y=_G(x,y’)‘]

Solution method Change of Variable, new dependent variable

Maple ✓
Mathematica ✓

ODE 116

y′(x) + tan(x)sec(x)cos2(y(x)) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 117

y′(x) = cot(x)cot(y(x))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 118

y′(x) + cot(x)cot(y(x)) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 119

y′(x) = sin(x)(csc(y(x)) − cot(y(x)))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 120

y′(x) = tan(x)cot(y(x))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 121

y′(x) + tan(x)cot(y(x)) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 122

y′(x) + sin(2x)csc(2y(x)) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 123

y′(x) = tan(x)(tan(y(x)) + sec(x)sec(y(x)))

[‘y=_G(x,y’)‘]

Solution method Exact equation, integrating factor

Maple ✓
Mathematica ✓

ODE 124

y′(x) = cos(x)sec2(y(x))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 125

y′(x) = sec2(x)sec3(y(x))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 126

y′(x) = a + bsin(y(x))

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple ✓
Mathematica ✓

ODE 127

y′(x) = a + bsin(Ax + By(x))

[[_homogeneous, ‘class C‘], _dAlembert]

Solution method Change of Variable, new dependent variable

Maple ✓
Mathematica ✓

ODE 128

y′(x) = tan(y(x))(cos(x)sin(y(x)) + 1)

[‘y=_G(x,y’)‘]

Solution method Change of Variable, new dependent variable

Maple ✗
Mathematica ✓

ODE 129

y′(x) + csc(2x)sin(2y(x)) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 130

f(x) + g(x)tan(y(x)) + y′(x) = 0

[‘y=_G(x,y’)‘]

Solution method Change of Variable, new dependent variable

Maple ✗
Mathematica ✗

ODE 131

y′(x) =

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple ✓
Mathematica ✓

ODE 132

y′(x) = ey(x) + x

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

Solution method Series solution to y′(x) = f(x,y(x)), case f(x,y) analytic

Maple ✓
Mathematica ✓

ODE 133

y′(x) = ey(x)+x

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 134

y′(x) = ex

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 135

y′(x) + y(x)log(x)log(y(x)) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 136

y′(x) = xm−1y(x)1−nf

[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]

Solution method Change of Variable, new dependent variable

Maple ✓
Mathematica ✓

ODE 137

y′(x) = af(y(x))

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple ✓
Mathematica ✓

ODE 138

y′(x) = f(a + bx + cy(x))

[[_homogeneous, ‘class C‘], _dAlembert]

Solution method Equation linear in the variables, y′(x) = f(a + bx + cy(x))

Maple ✓
Mathematica ✓

ODE 139

y′(x) = f(x)g(y(x))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 140

y′(x) = Csx(x)y(x)sec(x) + sec2(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 141

2y′(x) + 2csc2(x) = y(x)csc(x)sec(x) − y(x)2 sec2(x)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 142

2y′(x) = 2sin2(y(x))tan(y(x)) − xsin(2y(x))

[‘y=_G(x,y’)‘]

Solution method Change of Variable, new dependent variable

Maple ✗
Mathematica ✓

ODE 143

ax + 2y′(x) =

[[_homogeneous, ‘class G‘]]

Solution method Homogeneous equation, isobaric equation

Maple ✓
Mathematica ✓

ODE 144

3y′(x) = + x

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method Exact equation, integrating factor

Maple ✓
Mathematica ✓

ODE 145

xy′(x) =

[_quadrature]

Solution method Separable ODE, Dependent variable missing

Maple ✓
Mathematica ✓

ODE 146

xy′(x) + y(x) + x = 0

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 147

x2 + xy′(x) − y(x) = 0

[_linear]

Solution method Exact equation, integrating factor

Maple ✓
Mathematica ✓

ODE 148

xy′(x) = x3 − y(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 149

xy′(x) = x3 + y(x) + 1

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 150

xy′(x) = xm + y(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 151

xy′(x) = xsin(x) − y(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 152

xy′(x) = x2 sin(x) + y(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 153

xy′(x) = xn log(x) − y(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 154

xy′(x) = sin(x) − 2y(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 155

xy′(x) = ay(x)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 156

xy′(x) = ay(x) + x + 1

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 157

xy′(x) = ax + by(x)

[_linear]

Solution method Homogeneous equation

Maple ✓
Mathematica ✓

ODE 158

xy′(x) = ax2 + by(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 159

xy′(x) = a + bxn + cy(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 160

xy′(x) + (3 − x)y(x) + 2 = 0

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 161

(ax + 2)y(x) + xy′(x) + x = 0

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 162

y(x)(a + bx) + xy′(x) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 163

xy′(x) = x3 + y(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 164

xy′(x) = ax −y(x)

[_linear]

Solution method Linear ODE

Maple ✓
Mathematica ✓

ODE 165

y(x) + xy′(x) + x = 0

[_linear]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 166

x2 + xy′(x) + y(x)2 = 0

[_rational, _Riccati]

Solution method Riccati ODE, Special cases

Maple ✓
Mathematica ✓

ODE 167

xy′(x) = x2 + y(x)(y(x) + 1)

[[_homogeneous, ‘class D‘], _rational, _Riccati]

Solution method Riccati ODE, Special cases

Maple ✓
Mathematica ✓

ODE 168

xy′(x) + y(x)2 − y(x) = x2∕3

[_rational, _Riccati]

Solution method Riccati ODE, Special cases

Maple ✓
Mathematica ✓

ODE 169

xy′(x) = a + by(x)2

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 170

xy′(x) = ax2 + by(x)2 + y(x)

[[_homogeneous, ‘class D‘], _rational, _Riccati]

Solution method Riccati ODE, Special cases

Maple ✓
Mathematica ✓

ODE 171

xy′(x) = ax2n + y(x)(by(x) + n)

[_rational, _Riccati]

Solution method Riccati ODE, Special cases

Maple ✓
Mathematica ✓

ODE 172

xy′(x) = axn + by(x) + cy(x)2

[_rational, _Riccati]

Solution method Riccati ODE, Special cases

Maple ✓
Mathematica ✓

ODE 173

xy′(x) = axn + by(x) + cy(x)2 + k

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 174

a + xy′(x) + xy(x)2 = 0

[_rational, [_Riccati, _special]]

Solution method Riccati ODE, Main form

Maple ✓
Mathematica ✓

ODE 175

xy′(x) + y(x)(1 − xy(x)) = 0

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 176

xy′(x) = y(x)(1 − xy(x))

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 177

xy′(x) = y(x)(xy(x) + 1)

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 178

xy′(x) = ax3y(x)(1 − xy(x))

[_Bernoulli]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 179

xy′(x) = x3 + y(x) + xy(x)2

[[_homogeneous, ‘class D‘], _rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 180

xy′(x) = y(x)(2xy(x) + 1)

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 181

y(x)(axy(x) + 2) + bx + xy′(x) = 0

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 182

a0 + a1x + y(x)(a2 + a3xy(x)) + xy′(x) = 0

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 183

ax2y(x)2 + xy′(x) + 2y(x) = b

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 184

(n − m)y(x) + xm + xny(x)2 + xy′(x) = 0

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 185

y(x) + xy′(x) = 0

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 186

xy′(x) = axm − by(x) − cxny(x)2

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 187

xy′(x) = axn(x − y(x))2 − y(x) + 2x

[[_1st_order, _with_linear_symmetries], _rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 188

y(x)(1 − ay(x)log(x)) + xy′(x) = 0

[_Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 189

xy′(x) = f(x) + y(x)

[[_homogeneous, ‘class D‘], _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple ✓
Mathematica ✓

ODE 190

xy′(x) = y(x)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 191

xy′(x) + y(x) = 0

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 192

xy′(x) + y(x) = ay(x)3

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 193

xy′(x) = ay(x) + by(x)3

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 194

xy′(x) + 2y(x) = ax2ky(x)k

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple ✓
Mathematica ✓

ODE 195

xy′(x) = 4

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 196

xy′(x) + 2y(x) =

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 197

xy′(x) = + y(x)

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

Solution method Homogeneous equation

Maple ✓
Mathematica ✓

ODE 198

xy′(x) = + y(x)

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

Solution method Homogeneous equation

Maple ✓
Mathematica ✓

ODE 199

xy′(x) = x + y(x)

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

Solution method Homogeneous equation, xy′(x) = xf(x)g(u) + y(x)

Maple ✓
Mathematica ✓

ODE 200

xy′(x) = y(x) − x(x − y(x))

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

Solution method Homogeneous equation, xy′(x) = xf(x)g(u) + y(x)

Maple ✓
Mathematica ✓

ODE 201

xy′(x) = a∘ -2-2------2- b x + y(x) + y(x)

[[_homogeneous, ‘class A‘], _dAlembert]

Solution method Homogeneous equation

Maple ✓
Mathematica ✓

ODE 202

cos(y(x))( ) sin(y(x))− 3x2 cos(y (x )) + xy′(x) = 0

[‘y=_G(x,y’)‘]

Solution method Exact equation, integrating factor

Maple ✓
Mathematica ✓

ODE 203

xy′(x) − y(x) + xcos(y(x)) x + x = 0

[[_homogeneous, ‘class A‘], _dAlembert]

Solution method Homogeneous equation

Maple ✓
Mathematica ✓

ODE 204

xy′(x) = y(x) − xcos2( ) y(x) x

[[_homogeneous, ‘class A‘], _dAlembert]

Solution method Homogeneous equation

Maple ✓
Mathematica ✓

ODE 205

xy′(x) = ( ) 1− 2x2cot2(y(x))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple ✓
Mathematica ✓

ODE 206

xy′(x) = y(x) − cot2(y(x))

[_separable]

Solution method Homogeneous equation

Maple ✓
Mathematica ✓

ODE 207

xy′(x) + y(x) + 2xsec(xy(x)) = 0

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

Solution method Exact equation, integrating factor

Maple ✓
Mathematica ✓

ODE 208

xy′(x) − y(x) + xsec(y(x)) -x-- = 0

[[_homogeneous, ‘class A‘], _dAlembert]

Solution method Homogeneous equation

Maple ✓
Mathematica ✓

ODE 209

xy′(x) = y(x) + xsec2(y(x)) x

[[_homogeneous, ‘class A‘], _dAlembert]

Solution method Homogeneous equation

Maple ✓
Mathematica ✓

ODE 210

xy′(x) = sin(x − y(x))

[‘y=_G(x,y’)‘]

Solution method Change of Variable, new dependent variable

Maple ✗
Mathematica ✗

ODE 211

xy′(x) = y(x) + xsin( ) y(xx)

[[_homogeneous, ‘class A‘], _dAlembert]

Solution method Homogeneous equation

Maple ✓
Mathematica ✓

ODE 212

xy′(x) + tan(y(x)) = 0

[_separable]

Solution method Exact equation, integrating factor

Maple ✓
Mathematica ✓