3 Detailed lookup table and classification for each ODE

The following table 3 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 3: 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

 ′      2
y (x ) = x + 2y(x)+ 3 cosh (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 ) = a cos(bx + c)+ ky(x)

[[_linear, `class A`]]

Solution method Linear ODE

Maple
Mathematica



ODE 6

y′(x ) = a sin(bx + c)+ ky(x)

[[_linear, `class A`]]

Solution method Linear ODE

Maple
Mathematica



ODE 7

 ′           kx
y (x ) = a + be + cy(x)

[[_linear, `class A`]]

Solution method Linear ODE

Maple
Mathematica



ODE 8

         (        )
y′(x ) = x x2 − 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

 ′       n
y (x ) = ax y(x )

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 12

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 13

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 14

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 15

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 16

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 17

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 18

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 19

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 20

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 21

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

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 22

y′(x ) = 2 (cos(2x) cot2(x)− y(x )csc(2x ))

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 23

 ′              (         3  )
y (x ) = 4x csc(x) y(x )+ sin (x)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 24

y′(x ) = 4x csc(x) (y(x )− tan2(x)+ 1)

[_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

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 34

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 35

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 36

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 37

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 38

(ODEtools/info) missing specification of intermediate function

Solution method Linear ODE

Maple
Mathematica



ODE 39

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 40

[_Riccati]

Solution method Series solution to   , case   analytic

Maple
Mathematica



ODE 41

f(x)2 + y ′(x) = f′(x) + y(x)2

(ODEtools/info) missing specification of intermediate function

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

 ′              2
y (x ) = (y(x)+ x )

[[_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

 ′              2
y (x ) = (x − y(x)) + 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 ) = − x2 + 1 y(x)+  y(x )2 + 2x

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 47

 ′       ( 3   )   (  2      )
y (x ) = x x + 2  −  2x − y (x ) y(x)

[[_1st_order, _with_linear_symmetries], _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 48

         (     )   (         )
y′(x ) = x 2− x3  +  2x2 − y (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,

Maple
Mathematica



ODE 53

[[_homogeneous, `class C`], _Riccati]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 54

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 55

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica



ODE 56

[[_Riccati, _special]]

Solution method Riccati ODE, Main form

Maple
Mathematica



ODE 57

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 58

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 59

[[_Riccati, _special]]

Solution method Riccati ODE, Main form

Maple
Mathematica



ODE 60

[_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

 ′          2
y (x ) = ay(x) + 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

 ′        3  (   2   )            2
y (x ) = − x + 2x  + 1 y (x )− xy(x) − x + 1

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 66

         (                 )
y′(x ) = x x2y(x)− y(x)2 + 2

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 67

 ′                 2
y (x ) = − (1− x)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 (a+ by(x)2)

[_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

 ′           (    2         )
y (x ) = sin(x) 2sec (x)− y(x)

[_linear]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 73

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 74

[_linear]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 75

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 76

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 77

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 78

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica



ODE 79

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica



ODE 80

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica



ODE 81

           (          )
y′(x ) = y(x) a + by(x)2

[_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

 ′          3
y (x ) = xy(x)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 84

           (          )
y′(x )+ y(x) 1 − xy(x)2 =  0

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 85

 ′         2
y (x ) = y(x) (a+ bxy (x ))

[[_homogeneous, `class G`], _Abel]

Solution method Abel ODE, First kind

Maple
Mathematica



ODE 86

     (              )
y(x)3 a + 4b2x+ 3bx2  + y′(x )+ 3xy(x)2 = 0

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica



ODE 87

 ′         2(  3       )
y (x ) = y(x) x y (x )+ 1

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica



ODE 88

      (           )
2xy(x) axy (x)2 + 1 + y′(x) = 0

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 89

y′(x ) = y(x)2 − ax(1 − xn−1)y(x)3

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica



ODE 90

                      (         )
y′(x ) = ay(x)2 + xy(x)3 b+ cxn− 1

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica



ODE 91

y′(x )+ y(x)(y(x)2sec(x)+ tan(x)) = 0

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 92

y′(x )+ y(x)3tan(x)sec(x) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 93

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica



ODE 94

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 95

[[_homogeneous, `class G`], _Chini]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 96

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 97

[_Chini]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 98

[NONE]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 99

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica



ODE 100

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica



ODE 101

             ∘ ----
y′(x ) = ax + b y(x)

[[_homogeneous, `class G`], _Chini]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 102

               ----------
x3 + y′(x) = x∘ x4 + 4y(x)

[[_1st_order, _with_linear_symmetries]]

Solution method Homogeneous equation, isobaric equation

Maple
Mathematica



ODE 103

 ′      (     ∘ ----)
y (x )+ 2  1− x  y (x ) y(x) = 0

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 104

y′(x ) = ∘a-+-by(x)2

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica



ODE 105

           ∘ ---------
y′(x ) = y(x) a + by(x)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica



ODE 106

g(x)(f(x)− y(x))∘ (y(x)−-a)(y(x)−--b)-+ y′(x) = 0

[`y=_G(x,y')`]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 107

 ′     √ ----
y (x ) =  XY

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 108

          (  √ --)    (     √--)
y′(x ) = R1 x,  X   R2  y(x), Y

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

(ODEtools/info) missing specification of intermediate function

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 113

[`y=_G(x,y')`]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 114

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica



ODE 115

[`y=_G(x,y')`]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 116

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 117

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 118

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 119

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 120

[_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

 ′        2      3
y (x ) = sec (x)sec (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 ) = ∘a-+-bcos(y(x))

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica



ODE 132

 ′      y(x)
y (x ) = e   + x

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

Solution method Series solution to   , case   analytic

Maple
Mathematica



ODE 133

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 134

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 135

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 136

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 137

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica



ODE 138

[[_homogeneous, `class C`], _dAlembert]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 139

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 140

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 141

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

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 142

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

[`y=_G(x,y')`]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 143

       ′     ∘ -2-2------2---------
ax + 2y(x) =   a x  − 4bx − 4cy(x)

[[_homogeneous, `class G`]]

Solution method Homogeneous equation, isobaric equation

Maple
Mathematica



ODE 144

        ∘ ----------
3y′(x ) =  x2 − 3y(x)+ x

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 145

  ′     √ -2----2
xy (x) =  a  − 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

 2     ′
x  + 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) = x sin(x) − y(x)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 152

  ′       2
xy (x) = x sin(x) + y(x)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 153

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 154

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 155

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 156

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 157

[_linear]

Solution method Homogeneous equation

Maple
Mathematica



ODE 158

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 159

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 160

[_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

  ′       3  (      2)
xy (x) = x +  1−  2x  y(x)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 164

             (       )
xy′(x) = ax − 1 − bx2 y(x)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 165

(      2)         ′
 2 − ax  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

  ′       2
xy (x) = x + 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

  ′        n              2
xy (x) = ax + by(x) + cy(x )

[_rational, _Riccati]

Solution method Riccati ODE, Special cases

Maple
Mathematica



ODE 173

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 174

[_rational, [_Riccati, _special]]

Solution method Riccati ODE, Main form

Maple
Mathematica



ODE 175

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 176

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 177

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 178

[_Bernoulli]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 179

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 180

[[_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

  2    2     ′
ax y(x) +  xy(x) + 2y(x) = b

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 184

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

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 185

           n         ′
y(x)(a + bx 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

  ′        n         2
xy (x) = ax (x− y(x)) − 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 )(x2 − y(x)2) + y(x)

[[_homogeneous, `class D`], _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 190

             (        )
xy′(x) = y(x) y(x)2 + 1

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 191

xy′(x)+ y(x)(1 − xy(x)2) = 0

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 192

  ′             ( 2    )    3
xy (x)+ y(x) = a x  + 1 y(x)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 193

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 194

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 195

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 196

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 197

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 198

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 199

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

Solution method Homogeneous equation,

Maple
Mathematica



ODE 200

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

Solution method Homogeneous equation,

Maple
Mathematica



ODE 201

         ∘  ------------
xy′(x) = a  b2x2 + y(x)2 + y(x)

[[_homogeneous, `class A`], _dAlembert]

Solution method Homogeneous equation

Maple
Mathematica



ODE 202

cos(y(x))(sin (y(x)) − 3x2cos(y(x))) + xy′(x) = 0

[`y=_G(x,y')`]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 203

  ′                ( y(x))
xy (x)− y(x) + xcos  -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 − 2x2 cot2(y(x))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 206

  ′               2
xy (x) = y(x) − cot (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)- = 0
                      x

[[_homogeneous, `class A`], _dAlembert]

Solution method Homogeneous equation

Maple
Mathematica



ODE 209

                    (    )
xy′(x) = y(x) + xsec2 y(xx)-

[[_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(x)-
                      x

[[_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



ODE 213

[[_1st_order, _with_linear_symmetries]]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 214

[[_homogeneous, `class A`], _dAlembert]

Solution method Homogeneous equation

Maple
Mathematica



ODE 215

[`y=_G(x,y')`]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 216

[[_homogeneous, `class A`], _dAlembert]

Solution method Homogeneous equation

Maple
Mathematica



ODE 217

[[_homogeneous, `class A`], _dAlembert]

Solution method Homogeneous equation

Maple
Mathematica



ODE 218

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 219

[[_homogeneous, `class A`], _dAlembert]

Solution method Homogeneous equation

Maple
Mathematica



ODE 220

[[_homogeneous, `class G`]]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 221

                      (y(x))
xy′(x) = y(x) − 2xtanh -x--

[[_homogeneous, `class A`], _dAlembert]

Solution method Homogeneous equation

Maple
Mathematica



ODE 222

          ′             n
ny(x) + xy (x ) = f(x)g (x y(x))

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 223

xy′(x) = y(x)f (xmy (x )n)

[[_homogeneous, `class G`]]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 224

(x+  1)y′(x) = (3x + 4)x3 + y(x)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 225

(x+  1)y′(x) = 2y(x)+ (x + 1)4

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 226

(x+  1)y′(x) = ny(x)+ ex(x + 1)n+1

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 227

       ′                   2
(x+  1)y (x) = ay(x)+ bxy(x)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 228

(x+  1)y′(x)+ (x + 1)4y(x)3 + y(x) = 0

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 229

       ′          (         3)
(x+  1)y (x) = y(x) 1− xy (x)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 230

                    ∘ --------
(x+  1)y′(x) = (x + 1)  y(x)+  1+ y(x) + 1

[[_1st_order, _with_linear_symmetries]]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 231

        ′
(a+ x )y (x) = bx

[_quadrature]

Solution method Separable ODE, Dependent variable missing

Maple
Mathematica



ODE 232

(a+ x )y ′(x) = bx+ y(x)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 233

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 234

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 235

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 236

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 237

[_separable]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 238

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 239

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 240

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 241

              (        )
2xy′(x) = y (x ) y(x)2 + 1

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 242

2xy′(x)+ y(x)(y (x )2 + 1) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 243

   ′          (      2       )
2xy (x) = y (x ) − 6y(x) + x+ 1

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 244

∘ ---------------
  a2 − 4b− 4cy(x)+  a+ 2xy′(x)+ 4y (x ) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 245

         ′
(1− 2x )y (x) = 2(− 3y(x) + 16x+ 8)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 246

(2x+  1)y ′(x) = 4e−y(x) − 2

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 247

         ′            √ -----
2(1− x )y (x) = y(x)+ 4  1− xx

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 248

2(x+  1)y ′(x)+ (x + 1)4y(x)3 + 2y(x) = 0

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 249

3xy′(x) = 3x2∕3 + (1− 3y(x))y(x)

[_rational, _Riccati]

Solution method Riccati ODE, Special cases

Maple
Mathematica



ODE 250

              (         )
3xy′(x) = y (x ) xy(x)3 + 2

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 251

3xy′(x) = y (x )(3xy(x)3log(x)+ 1)

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 252

 2 ′
x y (x) = a − y(x)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 253

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 254

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 255

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 256

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 257

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 258

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 259

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 260

[[_homogeneous, `class A`], _rational, _Riccati]

Solution method Homogeneous equation

Maple
Mathematica



ODE 261

x2y′(x) = (− y(x)+ 2x + 1)2

[[_homogeneous, `class C`], _rational, _Riccati]

Solution method Equation linear in the variables,         (   )
y′(x) = f  XX1-
           2

Maple
Mathematica



ODE 262

x2y′(x) = a + by(x)2

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 263

 2 ′
x y (x) = y(x)(ay(x)+ x)

[[_homogeneous, `class A`], _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 264

x2y′(x) = y(x)(ax + by(x))

[[_homogeneous, `class A`], _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 265

  2                2    2 ′
ax  + bxy(x)+ cy(x) +  x y(x) = 0

[[_homogeneous, `class A`], _rational, _Riccati]

Solution method Homogeneous equation

Maple
Mathematica



ODE 266

x2y′(x) = a + bxn + x2y(x)2

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 267

 2 ′
x y (x)+ xy(x)(xy(x) + 4)+ 2 = 0

[[_homogeneous, `class G`], _rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 268

                           (      )
ax(1 − xy(x))+ x2y′(x)+ x2  − y(x)2 + 2 = 0

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 269

x2y′(x) = a + bx2y(x)2

[[_homogeneous, `class G`], _rational, [_Riccati, _special]]

Solution method Riccati ODE, Main form

Maple
Mathematica



ODE 270

x2y′(x) = a + bxn + cx2y(x)2

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 271

x2y′(x) = a + bxy(x)+ cx2y (x )2

[[_homogeneous, `class G`], _rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 272

 2 ′                    4   2
x y (x) = a + bxy(x)+ cx y (x )

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 273

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

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 274

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 275

[_rational, _Abel]

Solution method Abel ODE, Second kind

Maple
Mathematica



ODE 276

[_rational, _Abel]

Solution method Abel ODE, Second kind

Maple
Mathematica



ODE 277

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 278

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 279

[`y=_G(x,y')`]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 280

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 281

(      )
 1 − x2 y′(x)+ 1 = xy(x)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 282

(1 − x2)y′(x) = 5 − xy(x)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 283

    ( 2   )  ′
a +  x + 1  y(x)+  xy(x) = 0

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 284

    (     )
a +  x2 + 1 y′(x)−  xy(x) = 0

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 285

    (    2)  ′
a +  1− x   y(x)−  xy(x) = 0

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 286

(      )
 1 − x2 y′(x)+ xy (x )− x = 0

[_separable]

Solution method Linear ODE

Maple
Mathematica



ODE 287

(     2) ′      2
 1 − x  y (x)− x  + xy(x) = 0

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 288

(      )
 1 − x2 y′(x)+ x2 + xy(x) = 0

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 289

(x2 + 1)y′(x) = x (x2 + 1)− xy(x)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 290

(      )         (          )
 x2 + 1 y′(x) = x 3x2 − y(x)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 291

(1 − x2)y′(x)+ 2xy (x ) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 292

( 2    ) ′
 x  + 1 y (x) = 2x (x− y(x))

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 293

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 294

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 295

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 296

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 297

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 298

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 299

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 300

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 301

(      )         (                 )
 1 − x2 y′(x) = n y(x)2 − 2xy (x)+ 1

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 302

(x2 + 1)y′(x)+ x(1 − y(x))y(x ) = 0

[_separable]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 303

(     2) ′
 1 − x  y (x) = xy (x)(ay (x )+ 1)

[_separable]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 304

(      )                 (         )
 x2 + 1 y′(x) = y (x )2 − 2x y(x)2 + 1 y(x)+ 1

[_rational, _Abel]

Solution method Abel ODE, Second kind

Maple
Mathematica



ODE 305

( 2    ) ′                            ( 2    )   2
 x  + 1 y (x)+ x sin(y(x))cos(y(x)) = x x + 1  cos (y(x))

[`y=_G(x,y')`]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 306

(      )
 x2 + 1 y′(x) = x2 − y(x)cot−1(x) + 1

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 307

(     2) ′                       2
 4 − x  y (x)+ 4y(x) = (x+  2)y (x )

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 308

(       )
 a2 + x2 y′(x) = b + xy(x)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 309

                (             )
(a2 + x2)y′(x) =  √a2-+-x2 + x (b + y(x))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 310

(       )
 a2 + x2 y′(x)+ (x − y(x))y(x ) = 0

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 311

( 2    2) ′       2       2
 a  + x  y (x) = a − 2y(x) + 3xy (x)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 312

(       )
 a2 + x2 y′(x)+ bxy(x)2 + xy(x) = 0

[_separable]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 313

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 314

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 315

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 316

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 317

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 318

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 319

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 320

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 321

x2 + (x − 3)(x−  2)y ′(x)+ 3xy (x)− 8y(x) = 0

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 322

x(a + x)y′(x) = y(x)(b+ cy(x))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 323

      2 ′
(a+ x )y (x) = 2(a + x)(b+ y(x))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 324

k(− a+ y(x) + x)2 + (x − a)2y ′(x)+ y (x )2 = 0

[[_homogeneous, `class C`], _rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 325

              ′
(x−  a)(x − b)y(x) + ky(x) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 326

(x−  a)(x − b)y′(x) = y(x)(− a − b+ 2x )+ (x− a)(x − b)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 327

              ′          2
(x−  a)(x − b)y(x) = cy(x)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 328

k(y(x)− a)(y(x)−  b) + (x− a)(x − b)y′(x) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 329

k(− a+ y(x) + x)(− b+  y(x )+ x)+  (x − a)(x−  b)y′(x)+ y(x)2 = 0

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 330

2x2y′(x) = y(x)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 331

2x2y′(x)+ 2x2y(x) cot(x) + xcot(x)− 1 = 0

[_linear]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 332

  2 ′      2 (     2)
2x y (x)+ x   − y(x) + 2xy (x)+ 1 = 0

[[_homogeneous, `class G`], _rational, _Riccati]

Solution method Homogeneous equation, isobaric equation

Maple
Mathematica



ODE 333

[[_homogeneous, `class D`], _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 334

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 335

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 336

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 337

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 338

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 339

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 340

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 341

ax2y′(x) = axy (x)+ b2y(x)2 + x2

[[_homogeneous, `class A`], _rational, _Riccati]

Solution method Homogeneous equation

Maple
Mathematica



ODE 342

(a + bx2)y′(x) = A + By(x)2

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 343

(      2) ′
 a + bx  y (x) = cxy (x )log(y(x))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 344

x(ax + 1)y′(x) + a− y(x) = 0

[_separable]

Solution method Linear ODE

Maple
Mathematica



ODE 345

       2 ′         3               2
(a+ bx )y (x)+ y(x) (a+  bx )+ cy(x) = 0

[_rational, _Abel]

Solution method Abel ODE, Second kind

Maple
Mathematica



ODE 346

x3y′(x) = a + bx2y(x)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 347

 3 ′      2        2
x y (x) = x y(x) − x + 3

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 348

x3y′(x) = x4 + y(x)2

[[_homogeneous, `class G`], _rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 349

x3y′(x) = y(x) (x2 + y(x))

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 350

x3y′(x) = x2(y(x) − 1)+ y(x)2

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 351

x3y′(x) = (x + 1)y(x)2

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 352

 3 ′      2    (     2    )
x y (x)+ x y(x) 1 − x y(x) + 20 = 0

[[_homogeneous, `class G`], _rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 353

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 354

[[_homogeneous, `class A`], _rational, _Bernoulli]

Solution method Homogeneous equation

Maple
Mathematica



ODE 355

[`y=_G(x,y')`]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 356

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 357

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 358

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 359

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 360

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 361

  (     )        (         )
x 1 − x2 y ′(x) =  x2 − x + 1 y(x)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 362

x (1 − x2)y ′(x) = ax3 + (1 − 2x2)y (x )

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 363

  (    2)  ′     (     2)       (     2) 3
x 1 − x  y (x) =  1− 2x   y(x)+  1 − x  x

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 364

  (     )         (           )
x x2 + 1 y ′(x) = 2 1 − 2x2y(x)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 365

  ( 2   )  ′        (   2   )
x x  + 1 y (x) = x−  5x  + 3 y (x )

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 366

(      )        (      )
 1 − x2 xy ′(x)+  1 − x2 y(x )2 + x2 = 0

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 367

        2 ′                       2
(1− x )x y (x) = (2− x)xy(x) − y(x)

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 368

               (         )
2x3y′(x) = y(x) x2 − y(x)2

[[_homogeneous, `class A`], _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 369

2x3y′(x) = y(x) (ay(x)2 + 3x2)

[[_homogeneous, `class A`], _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 370

6x3y′(x) = 4x2y (x )+ (1− 3x )y(x)4

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 371

xy′(x)(a+  bx + cx2) − y(x)(a+  bx + cx2) + x2 = y(x )2

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 372

 4 ′          ( 3      )
x y (x) = y(x) x + y(x)

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 373

[_rational, [_Riccati, _special]]

Solution method Riccati ODE, Main form

Maple
Mathematica



ODE 374

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 375

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 376

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 377

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 378

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 379

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 380

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 381

x5y′(x) = 1 − 3x4y(x)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 382

x (1 − x4)y ′(x) = (1− x4) y(x)+ 2x (x2 − y(x)2)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 383

 7 ′       3    2    ( 2    )    3
x y (x)+ 5x y(x) +  2 x +  1 y(x) =  0

[_rational, _Abel]

Solution method Abel ODE, First kind

Maple
Mathematica



ODE 384

xny′(x) = a + bxn−1y(x)

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 385

 n ′       2n− 1      2
x y (x) = x    − y(x)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 386

    (           )
y(x) xn− 1 + y(x) + xny ′(x) + x2 = 0

[_Riccati]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 387

        n−1    2n− 2   n ′         2
(1− n )x    + x     + x y (x)+ y(x)  = 0

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 388

xny′(x) = a2x2n− 2 + b2y(x)2

[[_homogeneous, `class G`], _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica



ODE 389

xny′(x) = xn −1(ax2n − by(x)2 + ny(x))

[_rational, _Riccati]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 390

                           (                     )
x2ny′(x ) = − nxn− 1 + xny(x) x2ny(x)2 − 3xny(x) + 1 + 1

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica



ODE 391

xky′(x) = axm + by(x)n

[_Chini]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 392

√ ------′
  x2 + 1y (x) = 2x− y (x )

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 393

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 394

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 395

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 396

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 397

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 398

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 399

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 400

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 401

√ --       √ --
  Xy ′(x) =   Y

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 402

x3∕2y′(x) = a+  bx3∕2y(x)2

[_rational, [_Riccati, _special]]

Solution method Abel ODE, First kind

Maple
Mathematica



ODE 403

√ -3----′      ∘ ----3----
  x + 1y (x) =   y(x) + 1

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 404

∘ ----------------      ∘ ------------------------
  (1− x )x (1 − ax)y′(x) =  (1 − y(x))y(x)(1 − ay(x))

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 405

√ ----4-′      ∘ -------4-
  1− x y (x) =   1− y(x)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 406

√ -----------      ∘ ----------------
  x4 + x2 + 1y′(x ) = y(x)4 + y(x)2 + 1

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 407

√ -- ′
  Xy (x) = 0

[_quadrature]

Solution method Separable ODE, Dependent variable missing

Maple
Mathematica



ODE 408

√ --       √--
  Xy ′(x) +  Y  = 0

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 409

√Xy- ′(x) = √Y--

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 410

(      )2∕3       (        )2∕3
 x3 + 1    y′(x) +  y(x)3 + 1   = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 411

(a0 + a1x + 4x3)2∕3 y′(x) + (a0+ a1y(x) + 4y(x)3)2∕3 = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 412

  2∕3 ′       2∕3
X   y (x) = Y

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 413

[_Bernoulli]

Solution method Change of Variable, Two new variables

Maple
Mathematica



ODE 414

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 415

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 416

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 417

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 418

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 419

[_linear]

Solution method Linear ODE

Maple
Mathematica



ODE 420

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 421

  2
ex x+ y (x )y′(x) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 422

x3 + y(x)y′(x)+  y(x ) = 0

[_rational, [_Abel, `2nd type`, `class A`]]

Solution method Abel ODE, Second kind

Maple
Mathematica



ODE 423

                 ′
ax + by(x)+ y(x)y (x) = 0

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 424

y(x)y′(x )+ e−xx(y(x)+  1) = 0

[_separable]

Solution method Linear ODE

Maple
Mathematica



ODE 425

            ′
f(x)+  y(x )y (x) = g(x)y(x)

[[_Abel, `2nd type`, `class A`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 426

y(x)y′(x )+ y(x)2 + 4x(x + 1) = 0

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 427

     ′               2
y(x)y (x ) = ax + by(x)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 428

y(x)y′(x ) = ay(x)2 + bcos(c + x)

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 429

y(x)y′(x ) = a0 + a1y(x)+ a2y(x)2

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica



ODE 430

y(x)y′(x ) = ax + bxy(x)2

[_separable]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 431

y(x)y′(x ) = csc2(x)− y(x)2cot(x)

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 432

     ′     ∘ ----------
y(x)y (x ) =  a2 + y(x)2

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica



ODE 433

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica



ODE 434

[NONE]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 435

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 436

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 437

[[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 438

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 439

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 440

[[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 441

1−  y′(x) = y(x)+ x

[[_linear, `class A`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 442

(x−  y(x ))y′(x) = y (x )(2xy (x )+ 1)

[[_homogeneous, `class D`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 443

          ′
(y(x)+ x)y (x)+ tan(y(x)) = 0

[[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 444

                (    x     )
(x−  y(x ))y′(x) =  e−y(x) + 1 y(x)

[[_homogeneous, `class A`], _dAlembert]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 445

(y(x)+ x + 1)y′(x) + 3y(x)+ 4x + 1 = 0

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,         (   )
y′(x) = f  XX1-
           2

Maple
Mathematica



ODE 446

(y(x)+ x + 2)y′(x) = − y(x)− x + 1

[[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,  ′      ( X1)
y(x) = f  X2

Maple
Mathematica



ODE 447

                ′
(− y (x )− x + 3)y (x) = − 3y(x) + x+ 1

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,         (   )
y′(x) = f  XX12-

Maple
Mathematica



ODE 448

(y(x)− x + 3)y′(x) = 3y(x)−  4x+ 11

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,         (   )
y′(x) = f  X1-
          X2

Maple
Mathematica



ODE 449

           ′
(y(x)+ 2x)y (x)− 2y(x) + x = 0

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 450

(− y (x )+ 2x + 2)y′(x)+ 3 (− y(x)+ 2x + 1) = 0

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,         (   )
y′(x) = f  X1-
          X2

Maple
Mathematica



ODE 451

                 ′
(− y (x )+ 2x + 3)y(x)+ 2 = 0

[[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

Solution method Equation linear in the variables,  ′      ( X )
y(x) = f  X12-

Maple
Mathematica



ODE 452

(− y (x )+ 2x + 4)y′(x)− 2y (x )+ x + 5 = 0

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 453

[[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 454

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 455

[[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 456

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 457

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 458

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 459

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 460

[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]

Solution method Change of Variable, new independent variable

Maple
Mathematica



ODE 461

(         )
 x2 − y(x) y′(x) = 4xy (x)

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 462

y′(x )(y(x) − cot(x) csc(x))+ y (x )csc(x)(y(x)cos(x)+ 1 ) = 0

[[_Abel, `2nd type`, `class A`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 463

 2         ′        2
x  + 2y(x)y(x)+  y(x ) + 2x = 0

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

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 464

2y(x)y′(x ) = x3 + xy(x)2

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 465

           ′
(x−  2y(x ))y (x) = y(x )

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 466

(2y(x)+ x)y′(x)− y(x) + 2x = 0

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 467

           ′
(x−  2y(x ))y (x)+ y(x) + 2x = 0

[[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

Solution method Exact equation

Maple
Mathematica



ODE 468

(− 2y (x )+ x + 1)y′(x) = − y(x) + 2x + 1

[[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

Solution method Exact equation

Maple
Mathematica



ODE 469

(2y(x)+ x + 1)y′(x )− 2y(x)− x + 1 = 0

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,  ′      ( X1)
y(x) = f  X2

Maple
Mathematica



ODE 470

(2y(x)+ x + 1)y′(x )− 4y(x)+ x + 7 = 0

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,         (   )
y′(x) = f  XX1-
           2

Maple
Mathematica



ODE 471

x2 + 2(y (x )+ x)y′(x )+ 2y(x) = 0

[_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

Solution method Exact equation

Maple
Mathematica



ODE 472

                  ′
(− 2y (x )+ 2x + 3)y(x) = − 2y (x )+ 6x + 1

[[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 473

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 474

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 475

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 476

[_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

Solution method Exact equation

Maple
Mathematica



ODE 477

[[_Abel, `2nd type`, `class A`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 478

[[_Abel, `2nd type`, `class B`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 479

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 480

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 481

(x−  3y(x ))y′(x)− y(x) + 3x+  4 = 0

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,         (   )
y′(x) = f  XX1-
           2

Maple
Mathematica



ODE 482

(− 3y (x )− x + 4)y′(x)− 3y (x )− x + 3 = 0

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,  ′      ( X1)
y(x) = f  X2

Maple
Mathematica



ODE 483

                ′
(3y(x)+ 2x + 2)y (x ) = − 3y(x)− 2x + 1

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,         (   )
y′(x) = f  XX12-

Maple
Mathematica



ODE 484

(− 3y (x )− 2x + 5)y′(x)− 3y(x )− 2x + 1 = 0

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,         (   )
y′(x) = f  X1-
          X2

Maple
Mathematica



ODE 485

                  ′
(− 3y (x )+ 9x + 1)y(x)− y(x )+ 3x + 2 = 0

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,         (   )
y′(x) = f  XX12-

Maple
Mathematica



ODE 486

(4y(x)+ x)y′(x)− y(x) + 4x = 0

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,         (   )
y′(x) = f  X1-
          X2

Maple
Mathematica



ODE 487

                ′
(4y(x)+ 2x + 3)y (x ) = 2y(x) + x+ 1

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,  ′      ( X1)
y(x) = f  X2-

Maple
Mathematica



ODE 488

(− 4y (x )+ 2x + 5)y′(x) = − 2y (x )+ x + 3

[[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,         (   )
y′(x) = f  X1-
          X2

Maple
Mathematica



ODE 489

(− 4y (x )+ 3x + 5)y′(x) = − 3y (x )+ 7x + 2

[[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,  ′      ( X1)
y(x) = f  X2

Maple
Mathematica



ODE 490

4(− y (x )− x + 1)y′(x)− x + 2 = 0

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

Solution method Equation linear in the variables,         (   )
y′(x) = f  XX1-
           2

Maple
Mathematica



ODE 491

(− 4y (x )− 11x + 11)y′(x) = − 25y (x )− 8x + 62

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,  ′      ( X1)
y(x) = f  X2

Maple
Mathematica



ODE 492

                ′
(5y(x)+ 3x + 6)y (x ) = 7y(x) + x+ 2

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 493

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 494

[_rational, [_Abel, `2nd type`, `class A`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 495

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 496

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 497

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 498

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 499

[[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 500

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 501

(21y(x)+ 9x + 3)y′(x ) = − 5y(x)+ 7x + 45

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,         (   )
y′(x) = f  XX1-
           2

Maple
Mathematica



ODE 502

y′(x )(ax + by(x))+ x = 0

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

Solution method Change of Variable, new independent variable

Maple
Mathematica



ODE 503

 ′
y (x )(ax + by(x))+ y(x) = 0

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Change of Variable, new independent variable

Maple
Mathematica



ODE 504

y′(x )(ax + by(x))+ ay(x) + bx = 0

[[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

Solution method Exact equation

Maple
Mathematica



ODE 505

 ′
y (x )(ax + by(x)) = ay (x )+ bx

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,         (   )
y′(x) = f  XX12-

Maple
Mathematica



ODE 506

a1 + y′(x)(a2+ bx + c2y(x))+ by(x) + b1x = 0

[[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,         (   )
y′(x) = f  X1-
          X2

Maple
Mathematica



ODE 507

 ′
y (x )(a2 + b2y(x)+  c2y (x )) = a1 + b1x+  c1y (x )

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Solution method Equation linear in the variables,  ′      ( X1)
y(x) = f  X2-

Maple
Mathematica



ODE 508

xy(x)y′(x)+ y(x)2 + 1 = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 509

xy(x)y′(x) = y(x)2 + x

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

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 510

x2 + xy(x)y′(x) + y(x)2 = 0

[[_homogeneous, `class A`], _rational, _Bernoulli]

Solution method Homogeneous equation

Maple
Mathematica



ODE 511

x4 + xy(x)y′(x) − y(x)2 = 0

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 512

      ′        3            2
xy(x)y (x) = ax cos(x )+ y(x)

[[_homogeneous, `class D`], _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 513

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 514

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 515

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 516

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 517

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 518

[[_homogeneous, `class A`], _dAlembert]

Solution method Homogeneous equation

Maple
Mathematica



ODE 519

[[_homogeneous, `class A`], _dAlembert]

Solution method Homogeneous equation

Maple
Mathematica



ODE 520

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 521

x(y(x)+ 1)y′(x)− (1 − x)y(x) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 522

x(1−  y(x ))y′(x)+ (x + 1)y(x) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 523

           ′
x(1−  y(x ))y (x)+ (1 − x)y(x) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 524

ax + x(y(x)+ 2)y′(x) = 0

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 525

                   ′
(x(− y (x )) + 3x+ 2 )y (x)+ y(x) = 0

[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]

Solution method Change of Variable, new independent variable

Maple
Mathematica



ODE 526

x(y(x)+ 4)y′(x) = y(x )2 + 2y(x)+ 2x

[_rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation, special

Maple
Mathematica



ODE 527

           ′
x(a + y(x))y (x)+ bx + cy(x) = 0

[_rational, [_Abel, `2nd type`, `class B`]]

Solution method Change of Variable, new independent variable

Maple
Mathematica



ODE 528

x(a + y(x))y′(x) = y(x )(A + Bx )

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 529

x(y(x)+ x )y ′(x)+ y (x )2 = 0

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 530

x(x − y(x))y ′(x)+ y (x )2 = 0

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 531

x(y(x)+ x )y ′(x) = x2 + y(x)2

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 532

  2              ′                  2
2x  + x(x− y (x ))y (x)+ 3xy(x) − y(x) = 0

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 533

[[_homogeneous, `class A`], _dAlembert]

Solution method Homogeneous equation

Maple
Mathematica



ODE 534

[_rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation, special

Maple
Mathematica



ODE 535

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 536

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 537

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 538

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 539

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Change of Variable, new independent variable

Maple
Mathematica



ODE 540

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 541

(a+ x )(b + x)y′(x) = xy(x)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 542

−  2x3 + 2xy (x )y′(x)− y(x)2 + 1 = 0

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 543

           ′         2
a + 2xy(x)y(x) + y(x) = 0

[_separable]

Solution method Exact equation

Maple
Mathematica



ODE 544

2xy(x)y′(x) = ax + y(x)2

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 545

 2          ′         2
x  + 2xy(x)y(x) + y(x) = 0

[[_homogeneous, `class A`], _exact, _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 546

2xy(x)y′(x) = x2 + y(x)2

[[_homogeneous, `class A`], _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 547

       ′               2      2
2xy(x)y (x) = 4(2x + 1)x + y (x )

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 548

  (       )
x2 ax3 + 1  + 2xy(x)y′(x) = 6y(x)2

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 549

3x2 + (2xy (x)− x + 3)y′(x) + y(x)2 − y(x) = 0

[_exact, _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation

Maple
Mathematica



ODE 550

x(x − 2y(x))y ′(x)+ y (x )2 = 0

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 551

x(2y(x)+ x )y ′(x)+ (2x − y(x))y(x) = 0

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 552

             ′
x(x − 2y(x))y (x)+ (2x − y(x))y(x) = 0

[[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 553

[_rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 554

[_rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 555

[[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation

Maple
Mathematica



ODE 556

[_exact, _rational, _Bernoulli]

Solution method Exact equation

Maple
Mathematica



ODE 557

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 558

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 559

[_exact, _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation

Maple
Mathematica



ODE 560

[_exact, _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation

Maple
Mathematica



ODE 561

axy(x)y′(x) = x2 + y(x)2

[[_homogeneous, `class A`], _rational, _Bernoulli]

Solution method Homogeneous equation

Maple
Mathematica



ODE 562

axy(x)y′(x)+ x2 − y(x)2 = 0

[[_homogeneous, `class A`], _rational, _Bernoulli]

Solution method Homogeneous equation

Maple
Mathematica



ODE 563

  ′
xy (x)(a + by(x)) = cy(x)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 564

x(x − ay(x))y′(x) = y(x)(y (x )− ax)

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation

Maple
Mathematica



ODE 565

 ′
y (x )(x(Ax +  By(x))+ a0 + a1x + a2y(x)) = y(x )(Ax +  By(x))+ b0 + b1x + b2y(x)

[_rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation, Jacobi equation

Maple
Mathematica



ODE 566

y′(x )(x(a1 + b2x + c2y(x))+ a1 + b1x+  c1y (x )) = y(x)(a2+ b2x + c2y(x))+  a3+ b3x + c2y(x)

[_rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation, Jacobi equation

Maple
Mathematica



ODE 567

xy′(x)(ay(x)+ xn )+ y(x)2(b+ cy(x)) = 0

[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 568

(1 − x2y(x))y′(x)− xy(x)2 + 1 = 0

[_exact, _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation

Maple
Mathematica



ODE 569

(     2    ) ′          2
 1 − x y(x) y (x)+ xy(x)  − 1 = 0

[_rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation, special

Maple
Mathematica



ODE 570

x(1−  xy(x))y ′(x)+ y (x )(xy(x) + 1) = 0

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 571

             ′       3        2
x(xy(x) + 2)y (x) = 2x − xy (x ) − 2y(x)+ 3

[_exact, _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation

Maple
Mathematica



ODE 572

x(2−  xy(x))y ′(x)− x (xy (x)+ 1)y(x)2 + 2y(x) = 0

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class C`]]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 573

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 574

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 575

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 576

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 577

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 578

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 579

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Change of Variable, Two new variables

Maple
Mathematica



ODE 580

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Homogeneous equation, isobaric equation

Maple
Mathematica



ODE 581

    (                     )
y(x) − x2y(x)2 + 2xy (x )+ 1 + x(2xy(x)+ 1)y′(x) = 0

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class C`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 582

x2(x − 2y(x))y′(x) = 2x3 − 4xy (x )2 + y(x)3

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

Solution method Homogeneous equation

Maple
Mathematica



ODE 583

              ′         2
2x(x + 1)y(x)y(x) = y(x) + 1

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 584

3x2y(x)y′(x )+ 2xy(x)2 + 1 = 0

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

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 585

 2             ′         (  2                2)
x (4x − 3y(x))y (x) = y(x) 6x −  3xy(x)+ 2y(x)

[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

Solution method Homogeneous equation

Maple
Mathematica



ODE 586

(          )
 1 − x3y(x) y′(x) = x2y (x )2

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 587

      3     ′       2    2
a + 2x y(x)y(x) + 3x y(x) = 0

[[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

Solution method Exact equation

Maple
Mathematica



ODE 588

  (          )
x 3 − 2x2y(x) y ′(x) = 3x2y(x)2 − 3y(x) + 4x

[_exact, _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation

Maple
Mathematica



ODE 589

x (2x2y (x)+ 3)y ′(x)+ y (x )(3x2y(x)+ 4) = 0

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 590

3x4 + 8x3y(x)y′(x) − 6x2y(x)2 − y(x)4 = 0

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 591

xy(x)(a + bx2)y′(x) = A + By(x)2

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 592

  4     ′           3    2
3x y(x)y (x ) = 1 − 2x y(x)

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

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 593

[_rational, [_Abel, `2nd type`, `class B`]]

Solution method Abel ODE, Second kind

Maple
Mathematica



ODE 594

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 595

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 596

[[_Abel, `2nd type`, `class C`]]

Solution method Abel ODE, Second kind

Maple
Mathematica



ODE 597

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 598

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 599

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica



ODE 600

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica



ODE 601

(          )
 x2 + y(x)2 y′(x )+ xy(x) = 0

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 602

(x2 + y(x)2)y′(x ) = xy (x )

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 603

( 2       2) ′
 x  − y(x)  y (x ) = 2xy (x )

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 604

(          )
 x2 − y(x)2 y′(x )+ x(2y(x)+  x) = 0

[[_homogeneous, `class A`], _exact, _rational, _dAlembert]

Solution method Exact equation

Maple
Mathematica



ODE 605

( 2       2) ′
 x  + y(x)  y (x )+ 2x(y(x)+  2x) = 0

[[_homogeneous, `class A`], _exact, _rational, _dAlembert]

Solution method Exact equation

Maple
Mathematica



ODE 606

(               )
 − x2 + y(x )2 + 1 y′(x) = x2 − y(x)2 + 1

[[_1st_order, _with_linear_symmetries], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 607

( 2    2      2)  ′
 a  + x + y (x )  y(x) + 2xy(x) = 0

[_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

Solution method Exact equation

Maple
Mathematica



ODE 608

(              )
 a2 + x2 + y (x )2 y′(x) + b2 + x2 + 2xy(x) = 0

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica



ODE 609

(x2 + y(x)2 + x) y′(x) = y(x)

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 610

(           )
 3x2 − y(x)2 y′(x) = 2xy (x )

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

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 611

(x4 + y(x)2)y′(x ) = 4x3y (x )

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 612

              ′
y(x)(y(x)+ 1)y (x ) = x(x + 1)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 613

[_rational]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 614

[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 615

[_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

Solution method Exact equation

Maple
Mathematica



ODE 616

[[_1st_order, _with_linear_symmetries], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 617

[[_homogeneous, `class C`], _dAlembert]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 618

[[_homogeneous, `class C`], _dAlembert]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 619

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 620

[[_homogeneous, `class C`], _rational, _dAlembert]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 621

(y(x)+ x)2y′(x) = (y(x) + x+ 2)2

[[_homogeneous, `class C`], _rational, _dAlembert]

Solution method Equation linear in the variables,         (   )
y′(x) = f  XX1-
           2

Maple
Mathematica



ODE 622

(y(x)+ x)2y′(x) = x2 − 2xy(x) + 5y(x)2

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

Solution method Equation linear in the variables,  ′      ( X1)
y(x) = f  X2

Maple
Mathematica



ODE 623

 ′                   2             2
y (x )(a + b+ y(x) + x) = 2 (a + y(x))

[[_homogeneous, `class C`], _rational]

Solution method Equation linear in the variables,         (   )
y′(x) = f  XX12-

Maple
Mathematica



ODE 624

(                   )
 2x2 + 4xy(x) − y(x)2 y′(x) = x2 − 4xy(x)− 2y(x)2

[[_homogeneous, `class A`], _exact, _rational, _dAlembert]

Solution method Exact equation

Maple
Mathematica



ODE 625

          2 ′
(y(x)+ 3x) y (x) = 4y (x )(2y(x) + 3x)

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 626

(− y (x )− 3x + 1)2y ′(x) = (− 4y(x)− 6x+ 3)(1 − 2y(x))

[[_homogeneous, `class C`], _rational]

Solution method Change of Variable, Two new variables

Maple
Mathematica



ODE 627

 ′   (             2)      3
y (x ) cot(x )− 2y(x)  = y (x ) csc(x)sec(x)

[`y=_G(x,y')`]

Solution method Change of Variable, new independent variable

Maple
Mathematica



ODE 628

3y(x)2y′(x) = ay(x)3 + x+ 1

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 629

(x2 − 3y(x)2)y′(x)+ 2xy(x) + 1 = 0

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica



ODE 630

(            )
 2x2 + 3y(x)2 y′(x)+ x(y(x)+  3x) = 0

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

Solution method Exact equation

Maple
Mathematica



ODE 631

3(x2 − y(x)2)y′(x)− 2y(x)3 + 6x (x+ 1)y(x) + 3ex = 0

[`y=_G(x,y')`]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 632

(   2                2) ′       2               2
 3x  + 2xy(x) + 4y(x)  y(x) + 2x +  6xy(x)+ y(x)  = 0

[[_homogeneous, `class A`], _exact, _rational, _dAlembert]

Solution method Exact equation

Maple
Mathematica



ODE 633

[[_homogeneous, `class C`], _rational]

Solution method Equation linear in the variables,

Maple
Mathematica



ODE 634

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica



ODE 635

[_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`]]

Solution method Exact equation

Maple
Mathematica



ODE 636

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 637

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 638

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 639

[[_homogeneous, `class A`], _exact, _rational, _dAlembert]

Solution method Exact equation

Maple
Mathematica



ODE 640

[[_homogeneous, `class A`], _exact, _rational, _dAlembert]

Solution method Exact equation

Maple
Mathematica



ODE 641

  (        )       (      )
x 1 − y(x)2 y′(x) = x2 + 1 y(x)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 642

x (3x − y(x)2)y′(x)+ y(x) (5x− 2y (x )2) = 0

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 643

  ( 2      2) ′          ( 4    2      2)
x x  + y(x)  y (x) = y (x ) x + x + y(x)

[[_homogeneous, `class D`], _rational]

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

Maple
Mathematica



ODE 644

  (              )            (             )
x − x2 + y(x)2 + 1 y ′(x)+ y (x ) x2 − y(x)2 + 1 = 0

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

Solution method Homogeneous equation, special

Maple
Mathematica



ODE 645

  (    2       2) ′         (     2      2)
x a − x  − y(x)  y (x )+ y(x) a + x + y(x)   = 0

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

Solution method Homogeneous equation, special

Maple
Mathematica



ODE 646

  (          )            (           )
x 2x2 + y(x)2 y′(x) = y(x ) 2x2 + 3y (x )2

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 647

(  (     2      2)      )  ′         (     2      2)
 x  a− x  − y(x)  + y(x)  y(x) − y(x) a− x  − y(x)  + x = 0

[[_1st_order, _with_linear_symmetries], _rational]

Solution method Change of Variable, Two new variables

Maple
Mathematica



ODE 648

x(a + y(x))2y′(x) = by(x)2

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 649

x (x2 − xy(x) + y(x)2)y′(x )+ y(x)(x2 + xy(x)+ y(x)2) = 0

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 650

  (                 )           (                 )
x x2 − xy(x) − y(x)2 y′(x ) = y(x) x2 + xy(x) − y(x)2

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

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 651

x (axy (x)+ x2 + y(x)2)y′(x ) = y(x)(bxy (x )+ x2 + y(x)2)

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 652

  ( 2       2) ′          (  2      2)
x x  − 2y(x)  y (x) = y(x ) 2x − y (x )

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

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 653

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 654

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 655

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 656

[[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 657

[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 658

[[_homogeneous, `class G`], _exact, _rational]

Solution method Exact equation

Maple
Mathematica



ODE 659

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 660

[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

Solution method Change of Variable, new independent variable

Maple
Mathematica



ODE 661

6xy(x)2y′(x )+ 2y(x)3 + x = 0

[[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 662

x (6y (x )2 + x)y′(x)− 3y (x )3 + xy(x) = 0

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 663

  ( 2       2) ′           ( 2       2)
x x  − 6y(x)  y (x) = 4y(x ) x + 3y (x )

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 664

  (          )            (          )
x 3x − 7y(x)2 y ′(x)+ y (x ) 5x− 3y (x )2  = 0

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 665

 3    2    2 ′
x  + x y(x) y(x)−  x+ 1 = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 666

(           )
 1 − x2y(x)2 y′(x) = xy (x )3

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 667

(     2    2) ′         2
 1 − x y(x)  y (x) = y(x) (xy(x) + 1)

[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 668

  (         )
x xy (x)2 + 1 y′(x)+ y(x) = 0

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 669

x (xy (x)2 + 1)y′(x) = y(x)(2− 3xy (x)2)

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 670

                   (      )(          )
x2(a+  y(x ))2y′(x) = x2 + 1  a2 + y(x)2

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 671

(x2 + 1)(y(x)2 + 1)y′(x )+ 2xy(x)(1 − y(x)2) = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 672

( 2    )(    2    ) ′                    2
 x  + 1  y(x)  + 1 y (x )+ 2xy(x)(1− y (x ))  = 0

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 673

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica



ODE 674

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica



ODE 675

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 676

[[_homogeneous, `class G`], _rational]

Solution method Homogeneous equation, isobaric equation

Maple
Mathematica



ODE 677

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 678

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica



ODE 679

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 680

[[_homogeneous, `class A`], _exact, _rational, _dAlembert]

Solution method Exact equation

Maple
Mathematica



ODE 681

(                   )
 − x2y(x)− y (x )3 + x y′(x) = x3 + xy(x)2 − y(x)

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica



ODE 682

(a2x + y(x)(x2 − y(x)2))y′(x )+ x(x2 − y(x)2) = a2y(x)

[_rational]

Solution method Change of Variable, Two new variables

Maple
Mathematica



ODE 683

    (     2      2)  ′      (     2       2)
y(x) a + x + y (x )  y(x) = x a − x  − y(x)

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica



ODE 684

    (           )         (          )
y(x) 3x2 + y(x)2 y′(x )+ x x2 + 3y(x)2  = 0

[[_homogeneous, `class A`], _exact, _rational, _dAlembert]

Solution method Exact equation

Maple
Mathematica



ODE 685

    (      2      2)  ′      (     2      2)
y(x) a − 3x −  y(x )  y(x) + x a − x + y (x )  = 0

[_rational]

Solution method Change of Variable, Two new variables

Maple
Mathematica



ODE 686

2y(x)3y′(x) = x3 − xy(x)2

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

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 687

    (     2    ) ′       (  2   )
y(x) 2y(x)  + 1 y (x ) = x 2x + 1

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 688

         (           )
x3 + y(x) 3x2 + 2y(x )2  y′(x) = 0

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

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 689

y(x)(5x2 + 2y(x)2)y′(x )+ x (x2 + 5y(x)2) = 0

[[_homogeneous, `class A`], _exact, _rational, _dAlembert]

Solution method Exact equation

Maple
Mathematica



ODE 690

               (                           )
2x3 + 3x2y(x)+  − x3 + x2 + 3xy(x)2 + 2y(x)3 y′(x )− y(x)3 + y(x)2 = 0

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 691

4x3 + 9x2y(x)+ (3x3 + 6x2y(x)−  3xy(x)2 + 20y(x)3)y′(x)+ 6xy (x )2 − y(x)3 = 0

[[_homogeneous, `class A`], _exact, _rational, _dAlembert]

Solution method Exact equation

Maple
Mathematica



ODE 692

(           )
 ay(x)3 + x3 y′(x) = x2y (x )

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 693

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 694

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 695

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 696

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 697

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

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 698

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 699

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

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 700

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 701

  (                )
x 2y (x )3 + y(x)+ x  y′(x) = (x − y(x))y(x)

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 702

(− 7xy(x)3 − y (x )+ 5x)y ′(x)− y (x )4 + 5y(x) = 0

[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 703

    (      3    )    (          3)  ′
y(x) 1 − 2x y(x) + x  1− 2xy (x)  y(x) = 0

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 704

  (                    )
x − 2xy(x)3 − xy(x)2 + 2 y′(x) + 2y(x)+ 1 = 0

[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

Solution method Change of Variable, new independent variable

Maple
Mathematica



ODE 705

(     2    3       2    ) ′       (     4   )
 − 10x y(x) + 3y (x ) + 2 y (x) = x 5y(x) + 1

[_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

Solution method Exact equation

Maple
Mathematica



ODE 706

      (          )       (           )
xy′(x) a+  bxy (x)3 + y(x) a + cx3y(x) = 0

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 707

    (      3    2)    (      2   3)  ′
y(x) 1 − 2x y(x)  + x  1− 2x y (x )  y(x) = 0

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 708

            (          )                      (           )
x(1−  xy(x)) 1− x2y (x )2  y′(x) + y(x )(xy (x )+ 1) x2y(x)2 + 1 = 0

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 709

( 2       4) ′
 x  − y(x)  y (x ) = xy (x )

[[_homogeneous, `class G`], _rational]

Solution method Change of Variable, new independent variable

Maple
Mathematica



ODE 710

(          )
 x3 − y(x)4 y′(x ) = 3x2y (x )

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 711

(                   )
  a2x2 + (x2 + y(x)2)2 y′(x) = a2xy (x )

[_rational]

Solution method Change of Variable, Two new variables

Maple
Mathematica



ODE 712

 (         )
2 x − y(x)4 y′(x) = y (x )

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 713

[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 714

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

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 715

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 716

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 717

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 718

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 719

[[_homogeneous, `class G`], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 720

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 721

y′(x )(f1(x,y(x))+ xf2(x,y(x))) = y(x)f2(x,y(x))+ f3(x, y(x))

[NONE]

Solution method Homogeneous equation, Darbooux type

Maple
Mathematica



ODE 722

y′(x )(a(y(x) + x)+ 1)n + a(y(x )+ x)n = 0

[[_homogeneous, `class C`], _dAlembert]

Solution method Exact equation

Maple
Mathematica



ODE 723

xy′(x)(a+ xy (x)n)+ by(x) = 0

[[_homogeneous, `class G`], _rational]

Solution method Change of Variable, new independent variable

Maple
Mathematica



ODE 724

f(x)y(x)my ′(x)+ g (x )y(x)m+1 + h (x )y (x )n = 0

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica



ODE 725

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

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 726

∘ ----------      √ -------
  b2 − y (x )2y′(x) = a2 − x2

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 727

√ --′      √--
  Yy (x) =  X

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 728

( ∘ --------   )
    y(x)+ x + 1 y ′(x)+ 1 = 0

[[_homogeneous, `class C`], _dAlembert]

Solution method Change of Variable, new dependent variable

Maple
Mathematica



ODE 729

∘ ------′                ∘ ------
  xy(x)y (x)− y(x) + x =   xy(x)

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

Solution method Homogeneous equation

Maple
Mathematica



ODE 730

(     ∘ ------)
  x− 2  xy (x) y′(x) = y(x)

[[_homogeneous, `class A`], _dAlembert]

Solution method Homogeneous equation

Maple
Mathematica



ODE 731

(      )3∕2(      ∘  --------)
 x2 + 1     y(x)+    y(x )2 + 1  y′(x) = y(x)2 + 1

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 732

( 2    )3∕2(      ∘  ---2----)  ′         2
 x  + 1     y(x)+    y(x ) + 1  y(x) = y(x) + 1

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica



ODE 733

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

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 734

[`y=_G(x,y')`]

Solution method Exact equation, integrating factor

Maple
Mathematica



ODE 735

[[_homogeneous, `class G`], _dAlembert]

Solution method Homogeneous equation

Maple
Mathematica



ODE 736

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method Homogeneous equation

Maple
Mathematica



ODE 737

[NONE]
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