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

\(y'(x)=a f(x)\)

[_quadrature]

Solution method Separable ODE, Dependent variable missing

Maple
Mathematica

ODE 2

\(y'(x)=y(x)+x+\sin (x)\)

[[_linear, `class A`]]

Solution method Linear ODE

Maple
Mathematica

ODE 3

\(y'(x)=x^2+2 y(x)+3 \cosh (x)\)

[[_linear, `class A`]]

Solution method Linear ODE

Maple
Mathematica

ODE 4

\(y'(x)=a+b x+c y(x)\)

[[_linear, `class A`]]

Solution method Linear ODE

Maple
Mathematica

ODE 5

\(y'(x)=a \cos (b x+c)+k y(x)\)

[[_linear, `class A`]]

Solution method Linear ODE

Maple
Mathematica

ODE 6

\(y'(x)=a \sin (b x+c)+k y(x)\)

[[_linear, `class A`]]

Solution method Linear ODE

Maple
Mathematica

ODE 7

\(y'(x)=a+b e^{k x}+c y(x)\)

[[_linear, `class A`]]

Solution method Linear ODE

Maple
Mathematica

ODE 8

\(y'(x)=x \left (x^2-y(x)\right )\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 9

\(y'(x)=x \left (a y(x)+e^{-x^2}\right )\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 10

\(y'(x)=x^2 \left (a x^3+b y(x)\right )\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 11

\(y'(x)=a x^n y(x)\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 12

\(y'(x)=y(x) \cos (x)+\sin (x) \cos (x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 13

\(y'(x)=y(x) \cos (x)+e^{\sin (x)}\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 14

\(y'(x)=y(x) \cot (x)\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 15

\(y'(x)=1-y(x) \cot (x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 16

\(y'(x)=x \csc (x)-y(x) \cot (x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 17

\(y'(x)=y(x) (\cot (x)+2 \csc (2 x))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 18

\(y'(x)=\sec (x)-y(x) \cot (x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 19

\(y'(x)=y(x) \cot (x)+e^x \sin (x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 20

\(y'(x)+2 y(x) \cot (x)+\csc (x)=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 21

\(y'(x)=4 x \csc (x) \sec ^2(x)-2 y(x) \cot (2 x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 22

\(y'(x)=2 \left (\cos (2 x) \cot ^2(x)-y(x) \csc (2 x)\right )\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 23

\(y'(x)=4 x \csc (x) \left (y(x)+\sin ^3(x)\right )\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 24

\(y'(x)=4 x \csc (x) \left (y(x)-\tan ^2(x)+1\right )\)

[_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

\(y'(x)=y(x) \tan (x)+\sin (2 x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 32

\(y'(x)=\sin (2 x)-y(x) \tan (x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 33

\(y'(x)=2 y(x) \tan (x)+\sin (x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 34

\(y'(x)=2 (y(x) \tan (2 x)+\sec (2 x)+1)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 35

\(y'(x)=3 y(x) \tan (x)+\csc (x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 36

\(y'(x)=y(x) (a+\sin (\log (x))+\cos (\log (x)))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 37

\(y'(x)=6 e^{2 x}-y(x) \tanh (x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 38

\(y'(x)=y(x) f'(x)+f(x) f'(x)\)

(ODEtools/info) missing specification of intermediate function

Solution method Linear ODE

Maple
Mathematica

ODE 39

\(y'(x)=f(x)+g(x) y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 40

\(y'(x)=x^2-y(x)^2\)

[_Riccati]

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

Maple
Mathematica

ODE 41

\(f(x)^2+y'(x)=f'(x)+y(x)^2\)

(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

\(y'(x)=(y(x)+x)^2\)

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 44

\(y'(x)=(x-y(x))^2\)

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 45

\(y'(x)=(x-y(x))^2+3 (y(x)-x+1)\)

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

Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\)

Maple
Mathematica

ODE 46

\(y'(x)=-\left (x^2+1\right ) y(x)+y(x)^2+2 x\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 47

\(y'(x)=x \left (x^3+2\right )-\left (2 x^2-y(x)\right ) y(x)\)

[[_1st_order, _with_linear_symmetries], _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 48

\(y'(x)=x \left (2-x^3\right )+\left (2 x^2-y(x)\right ) y(x)+1\)

[[_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

\(y'(x)=y(x) (y(x)+\sin (2 x))+\cos (2 x)\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 51

\(y'(x)=x f(x) y(x)+f(x)+y(x)^2\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 52

\(y'(x)=(-4 y(x)+x+3)^2\)

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

Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\)

Maple
Mathematica

ODE 53

\(y'(x)=(9 y(x)+4 x+1)^2\)

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

Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\)

Maple
Mathematica

ODE 54

\(y'(x)=3 \left (a+b y(x)^2+b x\right )\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 55

\(y'(x)=a+b y(x)^2\)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica

ODE 56

\(y'(x)=a x+b y(x)^2\)

[[_Riccati, _special]]

Solution method Riccati ODE, Main form

Maple
Mathematica

ODE 57

\(y'(x)=a+b x+c y(x)^2\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 58

\(y'(x)=a x^{n-1}+b x^{2 n}+c y(x)^2\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 59

\(y'(x)=a x^2+b y(x)^2\)

[[_Riccati, _special]]

Solution method Riccati ODE, Main form

Maple
Mathematica

ODE 60

\(y'(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2\)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica

ODE 61

\(y'(x)=a y(x)+b y(x)^2+f(x)\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 62

\(y'(x)=a (x-y(x)) y(x)+1\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 63

\(y'(x)=a y(x)^2+f(x)+g(x) y(x)\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 64

\(y'(x)=x y(x) (y(x)+3)\)

[_separable]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 65

\(y'(x)=-x^3+\left (2 x^2+1\right ) y(x)-x y(x)^2-x+1\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 66

\(y'(x)=x \left (x^2 y(x)-y(x)^2+2\right )\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 67

\(y'(x)=-(1-x) y(x)^2+(1-2 x) y(x)+x\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 68

\(y'(x)=a x y(x)^2\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 69

\(y'(x)=x^n \left (a+b y(x)^2\right )\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 70

\(y'(x)=a x^m+b x^n y(x)^2\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 71

\(y'(x)=y(x) (a+b y(x) \cos (k x))\)

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 72

\(y'(x)=\sin (x) \left (2 \sec ^2(x)-y(x)\right )\)

[_linear]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 73

\(y'(x)+4 \csc (x)=y(x)^2 \sin (x)+y(x) (3-\cot (x))\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 74

\(y'(x)=y(x) \sec (x)+(\sin (x)-1)^2\)

[_linear]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 75

\(y'(x)+\left (1-y(x)^2\right ) \tan (x)=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 76

\(y'(x)=f(x)+g(x) y(x)+h(x) y(x)^2\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 77

\(y'(x)=f(x) \left (a+b y(x)+c y(x)^2\right )\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 78

\(y(x)^2 (a x+y(x))+y'(x)\)

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica

ODE 79

\(y'(x)=y(x)^2 \left (a e^x+y(x)\right )\)

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica

ODE 80

\(3 a (y(x)+2 x) y(x)^2+y'(x)=0\)

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica

ODE 81

\(y'(x)=y(x) \left (a+b y(x)^2\right )\)

[_quadrature]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 82

\(y'(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2+\text {a3} y(x)^3\)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica

ODE 83

\(y'(x)=x y(x)^3\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 84

\(y'(x)+y(x) \left (1-x y(x)^2\right )=0\)

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 85

\(y'(x)=y(x)^2 (a+b x y(x))\)

[[_homogeneous, `class G`], _Abel]

Solution method Abel ODE, First kind

Maple
Mathematica

ODE 86

\(y(x)^3 \left (a+4 b^2 x+3 b x^2\right )+y'(x)+3 x y(x)^2=0\)

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica

ODE 87

\(y'(x)=y(x)^2 \left (x^3 y(x)+1\right )\)

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica

ODE 88

\(2 x y(x) \left (a x y(x)^2+1\right )+y'(x)=0\)

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 89

\(y'(x)=y(x)^2-a x \left (1-x^{n-1}\right ) y(x)^3\)

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica

ODE 90

\(y'(x)=a y(x)^2+x y(x)^3 \left (b+c x^{n-1}\right )\)

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica

ODE 91

\(y'(x)+y(x) \left (y(x)^2 \sec (x)+\tan (x)\right )=0\)

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 92

\(y'(x)+y(x)^3 \tan (x) \sec (x)=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 93

\(y'(x)=\text {f0}(x)+\text {f1}(x) y(x)+\text {f2}(x) y(x)^2+\text {f3}(x) y(x)^3\)

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica

ODE 94

\(y'(x)=y(x) \left (y(x)^3 \sec (x)+\tan (x)\right )\)

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 95

\(y'(x)=a x^{\frac {n}{1-n}}+b y(x)^n\)

[[_homogeneous, `class G`], _Chini]

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 96

\(y'(x)=f(x) y(x)+g(x) y(x)^k\)

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 97

\(y'(x)=f(x)+g(x) y(x)+h(x) y(x)^n\)

[_Chini]

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 98

\(y'(x)=f(x) y(x)^m+g(x) y(x)^n\)

[NONE]

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 99

\(y'(x)=\sqrt {\left | y(x)\right | }\)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica

ODE 100

\(y'(x)=a+\sqrt {\text {A0}+\text {B0} y(x)}+b y(x)\)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica

ODE 101

\(y'(x)=a x+b \sqrt {y(x)}\)

[[_homogeneous, `class G`], _Chini]

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 102

\(x^3+y'(x)=x \sqrt {x^4+4 y(x)}\)

[[_1st_order, _with_linear_symmetries]]

Solution method Homogeneous equation, isobaric equation

Maple
Mathematica

ODE 103

\(y'(x)+2 \left (1-x \sqrt {y(x)}\right ) y(x)=0\)

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 104

\(y'(x)=\sqrt {a+b y(x)^2}\)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica

ODE 105

\(y'(x)=y(x) \sqrt {a+b y(x)}\)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica

ODE 106

\(g(x) (f(x)-y(x)) \sqrt {(y(x)-a) (y(x)-b)}+y'(x)=0\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 107

\(y'(x)=\sqrt {X Y}\)

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 108

\(y'(x)=\text {R1}\left (x,\sqrt {X}\right ) \text {R2}\left (y(x),\sqrt {Y}\right )\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 109

\(y'(x)=\cos ^2(x) \cos (y(x))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 110

\(y'(x)=\sec ^2(x) \text {Cosy}(y(x)) \cot (y(x))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 111

\(y'(x)=a+b \cos (A x+B y(x))\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 112

\(y'(x)=-\left (1-f'(x)\right ) \cos (y(x))+f'(x)-f(x) \sin (y(x))+1\)

(ODEtools/info) missing specification of intermediate function

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 113

\(g(x) \sin (a y(x))+h(x) \cos (a y(x))+f(x)+y'(x)=0\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 114

\(y'(x)=a+b \cos (y(x))\)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica

ODE 115

\(x \left (\sin (2 y(x))-x^2 \cos ^2(y(x))\right )+y'(x)=0\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 116

\(y'(x)+\tan (x) \sec (x) \cos ^2(y(x))=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 117

\(y'(x)=\cot (x) \cot (y(x))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 118

\(y'(x)+\cot (x) \cot (y(x))=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 119

\(y'(x)=\sin (x) (\csc (y(x))-\cot (y(x)))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 120

\(y'(x)=\tan (x) \cot (y(x))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 121

\(y'(x)+\tan (x) \cot (y(x))=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 122

\(y'(x)+\sin (2 x) \csc (2 y(x))=0\)

[_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

\(y'(x)=\cos (x) \sec ^2(y(x))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 125

\(y'(x)=\sec ^2(x) \sec ^3(y(x))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 126

\(y'(x)=a+b \sin (y(x))\)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica

ODE 127

\(y'(x)=a+b \sin (A x+B y(x))\)

[[_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

\(y'(x)+\csc (2 x) \sin (2 y(x))=0\)

[_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

\(y'(x)=\sqrt {a+b \cos (y(x))}\)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica

ODE 132

\(y'(x)=e^{y(x)}+x\)

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

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

Maple
Mathematica

ODE 133

\(y'(x)=e^{y(x)+x}\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 134

\(y'(x)=e^x \left (a+b e^{-y(x)}\right )\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 135

\(y'(x)+y(x) \log (x) \log (y(x))=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 136

\(y'(x)=x^{m-1} y(x)^{1-n} f\left (a x^m+b y(x)^n\right )\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 137

\(y'(x)=a f(y(x))\)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica

ODE 138

\(y'(x)=f(a+b x+c y(x))\)

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

Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\)

Maple
Mathematica

ODE 139

\(y'(x)=f(x) g(y(x))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 140

\(y'(x)=\text {Csx}(x) y(x) \sec (x)+\sec ^2(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 141

\(2 y'(x)+2 \csc ^2(x)=y(x) \csc (x) \sec (x)-y(x)^2 \sec ^2(x)\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 142

\(2 y'(x)=2 \sin ^2(y(x)) \tan (y(x))-x \sin (2 y(x))\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 143

\(a x+2 y'(x)=\sqrt {a^2 x^2-4 b x^2-4 c y(x)}\)

[[_homogeneous, `class G`]]

Solution method Homogeneous equation, isobaric equation

Maple
Mathematica

ODE 144

\(3 y'(x)=\sqrt {x^2-3 y(x)}+x\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 145

\(x y'(x)=\sqrt {a^2-x^2}\)

[_quadrature]

Solution method Separable ODE, Dependent variable missing

Maple
Mathematica

ODE 146

\(x y'(x)+y(x)+x=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 147

\(x^2+x y'(x)-y(x)=0\)

[_linear]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 148

\(x y'(x)=x^3-y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 149

\(x y'(x)=x^3+y(x)+1\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 150

\(x y'(x)=x^m+y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 151

\(x y'(x)=x \sin (x)-y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 152

\(x y'(x)=x^2 \sin (x)+y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 153

\(x y'(x)=x^n \log (x)-y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 154

\(x y'(x)=\sin (x)-2 y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 155

\(x y'(x)=a y(x)\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 156

\(x y'(x)=a y(x)+x+1\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 157

\(x y'(x)=a x+b y(x)\)

[_linear]

Solution method Homogeneous equation

Maple
Mathematica

ODE 158

\(x y'(x)=a x^2+b y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 159

\(x y'(x)=a+b x^n+c y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 160

\(x y'(x)+(3-x) y(x)+2=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 161

\((a x+2) y(x)+x y'(x)+x=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 162

\(y(x) (a+b x)+x y'(x)=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 163

\(x y'(x)=x^3+\left (1-2 x^2\right ) y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 164

\(x y'(x)=a x-\left (1-b x^2\right ) y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 165

\(\left (2-a x^2\right ) y(x)+x y'(x)+x=0\)

[_linear]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 166

\(x^2+x y'(x)+y(x)^2=0\)

[_rational, _Riccati]

Solution method Riccati ODE, Special cases

Maple
Mathematica

ODE 167

\(x y'(x)=x^2+y(x) (y(x)+1)\)

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

Solution method Riccati ODE, Special cases

Maple
Mathematica

ODE 168

\(x y'(x)+y(x)^2-y(x)=x^{2/3}\)

[_rational, _Riccati]

Solution method Riccati ODE, Special cases

Maple
Mathematica

ODE 169

\(x y'(x)=a+b y(x)^2\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 170

\(x y'(x)=a x^2+b y(x)^2+y(x)\)

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

Solution method Riccati ODE, Special cases

Maple
Mathematica

ODE 171

\(x y'(x)=a x^{2 n}+y(x) (b y(x)+n)\)

[_rational, _Riccati]

Solution method Riccati ODE, Special cases

Maple
Mathematica

ODE 172

\(x y'(x)=a x^n+b y(x)+c y(x)^2\)

[_rational, _Riccati]

Solution method Riccati ODE, Special cases

Maple
Mathematica

ODE 173

\(x y'(x)=a x^n+b y(x)+c y(x)^2+k\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 174

\(a+x y'(x)+x y(x)^2=0\)

[_rational, [_Riccati, _special]]

Solution method Riccati ODE, Main form

Maple
Mathematica

ODE 175

\(x y'(x)+y(x) (1-x y(x))=0\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 176

\(x y'(x)=y(x) (1-x y(x))\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 177

\(x y'(x)=y(x) (x y(x)+1)\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 178

\(x y'(x)=a x^3 y(x) (1-x y(x))\)

[_Bernoulli]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 179

\(x y'(x)=x^3+\left (2 x^2+1\right ) y(x)+x y(x)^2\)

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 180

\(x y'(x)=y(x) (2 x y(x)+1)\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 181

\(y(x) (a x y(x)+2)+b x+x y'(x)=0\)

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 182

\(\text {a0}+\text {a1} x+y(x) (\text {a2}+\text {a3} x y(x))+x y'(x)=0\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 183

\(a x^2 y(x)^2+x y'(x)+2 y(x)=b\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 184

\(\frac {1}{2} (n-m) y(x)+x^m+x^n y(x)^2+x y'(x)=0\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 185

\(y(x) \left (a+b x^n y(x)\right )+x y'(x)=0\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 186

\(x y'(x)=a x^m-b y(x)-c x^n y(x)^2\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 187

\(x y'(x)=a x^n (x-y(x))^2-y(x)+2 x\)

[[_1st_order, _with_linear_symmetries], _rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 188

\(y(x) (1-a y(x) \log (x))+x y'(x)=0\)

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 189

\(x y'(x)=f(x) \left (x^2-y(x)^2\right )+y(x)\)

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 190

\(x y'(x)=y(x) \left (y(x)^2+1\right )\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 191

\(x y'(x)+y(x) \left (1-x y(x)^2\right )=0\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 192

\(x y'(x)+y(x)=a \left (x^2+1\right ) y(x)^3\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 193

\(x y'(x)=a y(x)+b \left (x^2+1\right ) y(x)^3\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 194

\(x y'(x)+2 y(x)=a x^{2 k} y(x)^k\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 195

\(x y'(x)=4 \left (y(x)-\sqrt {y(x)}\right )\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 196

\(x y'(x)+2 y(x)=\sqrt {y(x)^2+1}\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 197

\(x y'(x)=\sqrt {x^2+y(x)^2}+y(x)\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 198

\(x y'(x)=\sqrt {x^2-y(x)^2}+y(x)\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 199

\(x y'(x)=x \sqrt {x^2+y(x)^2}+y(x)\)

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

Solution method Homogeneous equation, \(xy'(x)=x f(x) g(u)+y(x)\)

Maple
Mathematica

ODE 200

\(x y'(x)=y(x)-x (x-y(x)) \sqrt {x^2+y(x)^2}\)

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

Solution method Homogeneous equation, \(xy'(x)=x f(x) g(u)+y(x)\)

Maple
Mathematica

ODE 201

\(x y'(x)=a \sqrt {b^2 x^2+y(x)^2}+y(x)\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 202

\(\cos (y(x)) \left (\sin (y(x))-3 x^2 \cos (y(x))\right )+x y'(x)=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 203

\(x y'(x)-y(x)+x \cos \left (\frac {y(x)}{x}\right )+x=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 204

\(x y'(x)=y(x)-x \cos ^2\left (\frac {y(x)}{x}\right )\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 205

\(x y'(x)=\left (1-2 x^2\right ) \cot ^2(y(x))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 206

\(x y'(x)=y(x)-\cot ^2(y(x))\)

[_separable]

Solution method Homogeneous equation

Maple
Mathematica

ODE 207

\(x y'(x)+y(x)+2 x \sec (x y(x))=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 208

\(x y'(x)-y(x)+x \sec \left (\frac {y(x)}{x}\right )=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 209

\(x y'(x)=y(x)+x \sec ^2\left (\frac {y(x)}{x}\right )\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 210

\(x y'(x)=\sin (x-y(x))\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 211

\(x y'(x)=y(x)+x \sin \left (\frac {y(x)}{x}\right )\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 212

\(x y'(x)+\tan (y(x))=0\)

[_separable]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 213

\(x y'(x)+\tan (y(x)+x)+x=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 214

\(x y'(x)=y(x)-x \tan \left (\frac {y(x)}{x}\right )\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 215

\(x y'(x)=\left (y(x)^2+1\right ) \left (x^2+\tan ^{-1}(y(x))\right )\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 216

\(x y'(x)=x e^{\frac {y(x)}{x}}+y(x)\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 217

\(x y'(x)=x e^{\frac {y(x)}{x}}+y(x)+x\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 218

\(x y'(x)=y(x) \log (y(x))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 219

\(x y'(x)=y(x) (-\log (y(x))+\log (x)+1)\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 220

\(x y'(x)+y(x) (-\log (y(x))-\log (x)+1)=0\)

[[_homogeneous, `class G`]]

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 221

\(x y'(x)=y(x)-2 x \tanh \left (\frac {y(x)}{x}\right )\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 222

\(n y(x)+x y'(x)=f(x) g\left (x^n y(x)\right )\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 223

\(x y'(x)=y(x) f\left (x^m y(x)^n\right )\)

[[_homogeneous, `class G`]]

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 224

\((x+1) y'(x)=(3 x+4) x^3+y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 225

\((x+1) y'(x)=2 y(x)+(x+1)^4\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 226

\((x+1) y'(x)=n y(x)+e^x (x+1)^{n+1}\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 227

\((x+1) y'(x)=a y(x)+b x y(x)^2\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 228

\((x+1) y'(x)+(x+1)^4 y(x)^3+y(x)=0\)

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 229

\((x+1) y'(x)=y(x) \left (1-x y(x)^3\right )\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 230

\((x+1) y'(x)=(x+1) \sqrt {y(x)+1}+y(x)+1\)

[[_1st_order, _with_linear_symmetries]]

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 231

\((a+x) y'(x)=b x\)

[_quadrature]

Solution method Separable ODE, Dependent variable missing

Maple
Mathematica

ODE 232

\((a+x) y'(x)=b x+y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 233

\((a+x) y'(x)+b x^2+y(x)=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 234

\((a+x) y'(x)=2 (a+x)^5+3 y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 235

\((a+x) y'(x)=b+c y(x)\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 236

\((a+x) y'(x)=b x+c y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 237

\((a+x) y'(x)=y(x) (1-a y(x))\)

[_separable]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 238

\((a-x) y'(x)=y(x)^3 (b+c x)+y(x)\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 239

\(2 x y'(x)=2 x^3-y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 240

\(2 x y'(x)+1=y(x)^2+4 i x y(x)\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 241

\(2 x y'(x)=y(x) \left (y(x)^2+1\right )\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 242

\(2 x y'(x)+y(x) \left (y(x)^2+1\right )=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 243

\(2 x y'(x)=y(x) \left (-6 y(x)^2+x+1\right )\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 244

\(\sqrt {a^2-4 b-4 c y(x)}+a+2 x y'(x)+4 y(x)=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 245

\((1-2 x) y'(x)=2 (-3 y(x)+16 x+8)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 246

\((2 x+1) y'(x)=4 e^{-y(x)}-2\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 247

\(2 (1-x) y'(x)=y(x)+4 \sqrt {1-x} x\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 248

\(2 (x+1) y'(x)+(x+1)^4 y(x)^3+2 y(x)=0\)

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 249

\(3 x y'(x)=3 x^{2/3}+(1-3 y(x)) y(x)\)

[_rational, _Riccati]

Solution method Riccati ODE, Special cases

Maple
Mathematica

ODE 250

\(3 x y'(x)=y(x) \left (x y(x)^3+2\right )\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 251

\(3 x y'(x)=y(x) \left (3 x y(x)^3 \log (x)+1\right )\)

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 252

\(x^2 y'(x)=a-y(x)\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 253

\(x^2 y'(x)=a+b x+c x^2+x y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 254

\(x^2 y'(x)=a+b x+c x^2-x y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 255

\(x^2 y'(x)+(1-2 x) y(x)=x^2\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 256

\(x^2 y'(x)=a+b x y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 257

\(x^2 y'(x)=y(x) (a+b x)\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 258

\(x^2 y'(x)+(x+2) x y(x)=\left (1-e^{-2 x}\right ) x-2\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 259

\(x^2 y'(x)+2 (1-x) x y(x)=e^x \left (2 e^x-1\right )\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 260

\(x^2 y'(x)+x^2+x y(x)+y(x)^2=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 261

\(x^2 y'(x)=(-y(x)+2 x+1)^2\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 262

\(x^2 y'(x)=a+b y(x)^2\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 263

\(x^2 y'(x)=y(x) (a y(x)+x)\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 264

\(x^2 y'(x)=y(x) (a x+b y(x))\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 265

\(a x^2+b x y(x)+c y(x)^2+x^2 y'(x)=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 266

\(x^2 y'(x)=a+b x^n+x^2 y(x)^2\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 267

\(x^2 y'(x)+x y(x) (x y(x)+4)+2=0\)

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 268

\(a x (1-x y(x))+x^2 y'(x)+x^2 \left (-y(x)^2\right )+2=0\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 269

\(x^2 y'(x)=a+b x^2 y(x)^2\)

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

Solution method Riccati ODE, Main form

Maple
Mathematica

ODE 270

\(x^2 y'(x)=a+b x^n+c x^2 y(x)^2\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 271

\(x^2 y'(x)=a+b x y(x)+c x^2 y(x)^2\)

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 272

\(x^2 y'(x)=a+b x y(x)+c x^4 y(x)^2\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 273

\(x^2 y'(x)+y(x) \left (x^2+y(x)^2-x\right )=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 274

\(x^2 y'(x)=2 y(x) \left (x-y(x)^2\right )\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 275

\(x^2 y'(x)=a x^2 y(x)^2-a y(x)^3\)

[_rational, _Abel]

Solution method Abel ODE, Second kind

Maple
Mathematica

ODE 276

\(a y(x)^2+b x^2 y(x)^3+x^2 y'(x)=0\)

[_rational, _Abel]

Solution method Abel ODE, Second kind

Maple
Mathematica

ODE 277

\(x^2 y'(x)=y(x) \left (a x+b y(x)^3\right )\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 278

\(x^2 y'(x)+x y(x)+\sqrt {y(x)}=0\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 279

\(x^2 y'(x)=3 x \tan (y(x))+\sec (y(x))\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 280

\(\left (1-x^2\right ) y'(x)=-x^2+y(x)+1\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 281

\(\left (1-x^2\right ) y'(x)+1=x y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 282

\(\left (1-x^2\right ) y'(x)=5-x y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 283

\(a+\left (x^2+1\right ) y'(x)+x y(x)=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 284

\(a+\left (x^2+1\right ) y'(x)-x y(x)=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 285

\(a+\left (1-x^2\right ) y'(x)-x y(x)=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 286

\(\left (1-x^2\right ) y'(x)+x y(x)-x=0\)

[_separable]

Solution method Linear ODE

Maple
Mathematica

ODE 287

\(\left (1-x^2\right ) y'(x)-x^2+x y(x)=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 288

\(\left (1-x^2\right ) y'(x)+x^2+x y(x)=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 289

\(\left (x^2+1\right ) y'(x)=x \left (x^2+1\right )-x y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 290

\(\left (x^2+1\right ) y'(x)=x \left (3 x^2-y(x)\right )\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 291

\(\left (1-x^2\right ) y'(x)+2 x y(x)=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 292

\(\left (x^2+1\right ) y'(x)=2 x (x-y(x))\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 293

\(\left (x^2+1\right ) y'(x)=2 x \left (x^2+1\right )^2+2 x y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 294

\(\left (1-x^2\right ) y'(x)+\cos (x)=2 x y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 295

\(\left (x^2+1\right ) y'(x)=\tan (x)-2 x y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 296

\(\left (1-x^2\right ) y'(x)=a+4 x y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 297

\(\left (x^2+1\right ) y'(x)=y(x) (a+2 b x)\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 298

\(\left (x^2+1\right ) y'(x)=y(x)^2+1\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 299

\(\left (1-x^2\right ) y'(x)=1-y(x)^2\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 300

\(\left (1-x^2\right ) y'(x)=1-(2 x-y(x)) y(x)\)

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 301

\(\left (1-x^2\right ) y'(x)=n \left (y(x)^2-2 x y(x)+1\right )\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 302

\(\left (x^2+1\right ) y'(x)+x (1-y(x)) y(x)=0\)

[_separable]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 303

\(\left (1-x^2\right ) y'(x)=x y(x) (a y(x)+1)\)

[_separable]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 304

\(\left (x^2+1\right ) y'(x)=y(x)^2-2 x \left (y(x)^2+1\right ) y(x)+1\)

[_rational, _Abel]

Solution method Abel ODE, Second kind

Maple
Mathematica

ODE 305

\(\left (x^2+1\right ) y'(x)+x \sin (y(x)) \cos (y(x))=x \left (x^2+1\right ) \cos ^2(y(x))\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 306

\(\left (x^2+1\right ) y'(x)=x^2-y(x) \cot ^{-1}(x)+1\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 307

\(\left (4-x^2\right ) y'(x)+4 y(x)=(x+2) y(x)^2\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 308

\(\left (a^2+x^2\right ) y'(x)=b+x y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 309

\(\left (a^2+x^2\right ) y'(x)=\left (\sqrt {a^2+x^2}+x\right ) (b+y(x))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 310

\(\left (a^2+x^2\right ) y'(x)+(x-y(x)) y(x)=0\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 311

\(\left (a^2+x^2\right ) y'(x)=a^2-2 y(x)^2+3 x y(x)\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 312

\(\left (a^2+x^2\right ) y'(x)+b x y(x)^2+x y(x)=0\)

[_separable]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 313

\((1-x) x y'(x)=a+(x+1) y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 314

\((1-x) x y'(x)=2 (x y(x)+1)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 315

\((1-x) x y'(x)=2 (x y(x)-1)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 316

\(x (x+1) y'(x)=(1-2 x) y(x)\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 317

\((1-x) x y'(x)+(2 x+1) y(x)=a\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 318

\((1-x) x y'(x)=a+2 (2-x) y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 319

\((1-x) x y'(x)-3 x y(x)+y(x)+2=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 320

\(x (x+1) y'(x)=\left (x^2+x-1\right ) y(x)+(x+1) \left (x^2-1\right )\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 321

\(x^2+(x-3) (x-2) y'(x)+3 x y(x)-8 y(x)=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 322

\(x (a+x) y'(x)=y(x) (b+c y(x))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 323

\((a+x)^2 y'(x)=2 (a+x) (b+y(x))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 324

\(k (-a+y(x)+x)^2+(x-a)^2 y'(x)+y(x)^2=0\)

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 325

\((x-a) (x-b) y'(x)+k y(x)=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 326

\((x-a) (x-b) y'(x)=y(x) (-a-b+2 x)+(x-a) (x-b)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 327

\((x-a) (x-b) y'(x)=c y(x)^2\)

[_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

\(2 x^2 y'(x)=y(x)\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 331

\(2 x^2 y'(x)+2 x^2 y(x) \cot (x)+x \cot (x)-1=0\)

[_linear]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 332

\(2 x^2 y'(x)+x^2 \left (-y(x)^2\right )+2 x y(x)+1=0\)

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

Solution method Homogeneous equation, isobaric equation

Maple
Mathematica

ODE 333

\(2 x^2 y'(x)=\left (x^2-y(x)^2\right ) (1-x \cot (x))+2 x y(x)\)

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 334

\(2 \left (1-x^2\right ) y'(x)=\sqrt {1-x^2}+(x+1) y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 335

\((1-2 x) x y'(x)+(1-4 x) y(x)+1=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 336

\((1-2 x) x y'(x)=y(x)^2-(4 x+1) y(x)+4 x\)

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 337

\(2 (1-x) x y'(x)+(1-2 x) y(x)+x=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 338

\(2 (1-x) x y'(x)+(1-x) y(x)^2+x=0\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 339

\(2 \left (x^2+x+1\right ) y'(x)=8 x^2-(2 x+1) y(x)+1\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 340

\(4 \left (x^2+1\right ) y'(x)-x^2-4 x y(x)=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 341

\(a x^2 y'(x)=a x y(x)+b^2 y(x)^2+x^2\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 342

\(\left (a+b x^2\right ) y'(x)=A+B y(x)^2\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 343

\(\left (a+b x^2\right ) y'(x)=c x y(x) \log (y(x))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 344

\(x (a x+1) y'(x)+a-y(x)=0\)

[_separable]

Solution method Linear ODE

Maple
Mathematica

ODE 345

\((a+b x)^2 y'(x)+y(x)^3 (a+b x)+c y(x)^2=0\)

[_rational, _Abel]

Solution method Abel ODE, Second kind

Maple
Mathematica

ODE 346

\(x^3 y'(x)=a+b x^2 y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 347

\(x^3 y'(x)=x^2 y(x)-x^2+3\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 348

\(x^3 y'(x)=x^4+y(x)^2\)

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 349

\(x^3 y'(x)=y(x) \left (x^2+y(x)\right )\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 350

\(x^3 y'(x)=x^2 (y(x)-1)+y(x)^2\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 351

\(x^3 y'(x)=(x+1) y(x)^2\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 352

\(x^3 y'(x)+x^2 y(x) \left (1-x^2 y(x)\right )+20=0\)

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 353

\(x^6 \left (-y(x)^2\right )+x^3 y'(x)+(3-2 x) x^2 y(x)+3=0\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 354

\(x^3 y'(x)=y(x) \left (2 x^2+y(x)^2\right )\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 355

\(x^3 y'(x)=\cos (y(x)) \left (\cos (y(x))-2 x^2 \sin (y(x))\right )\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 356

\(x \left (x^2+1\right ) y'(x)=a x^2+y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 357

\(x \left (1-x^2\right ) y'(x)=a x^2+y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 358

\(x \left (x^2+1\right ) y'(x)=a x^3+y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 359

\(x \left (x^2+1\right ) y'(x)=a-x^2 y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 360

\(x \left (x^2+1\right ) y'(x)=\left (1-x^2\right ) y(x)\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 361

\(x \left (1-x^2\right ) y'(x)=\left (x^2-x+1\right ) y(x)\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 362

\(x \left (1-x^2\right ) y'(x)=a x^3+\left (1-2 x^2\right ) y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 363

\(x \left (1-x^2\right ) y'(x)=\left (1-2 x^2\right ) y(x)+\left (1-x^2\right ) x^3\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 364

\(x \left (x^2+1\right ) y'(x)=2 \left (1-2 x^2 y(x)\right )\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 365

\(x \left (x^2+1\right ) y'(x)=x-\left (5 x^2+3\right ) y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 366

\(\left (1-x^2\right ) x y'(x)+\left (1-x^2\right ) y(x)^2+x^2=0\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 367

\((1-x) x^2 y'(x)=(2-x) x y(x)-y(x)^2\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 368

\(2 x^3 y'(x)=y(x) \left (x^2-y(x)^2\right )\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 369

\(2 x^3 y'(x)=y(x) \left (a y(x)^2+3 x^2\right )\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 370

\(6 x^3 y'(x)=4 x^2 y(x)+(1-3 x) y(x)^4\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 371

\(x y'(x) \left (a+b x+c x^2\right )-y(x) \left (a+b x+c x^2\right )+x^2=y(x)^2\)

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 372

\(x^4 y'(x)=y(x) \left (x^3+y(x)\right )\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 373

\(a^2+x^4 y'(x)+x^4 y(x)^2=0\)

[_rational, [_Riccati, _special]]

Solution method Riccati ODE, Main form

Maple
Mathematica

ODE 374

\(x^4 y'(x)+x^3 y(x)+\csc (x y(x))=0\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 375

\(\left (1-x^4\right ) y'(x)=2 x \left (1-y(x)^2\right )\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 376

\(x \left (1-x^3\right ) y'(x)=2 x-\left (1-4 x^3\right ) y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 377

\(x \left (1-x^3\right ) y'(x)=x^2+y(x) (1-2 x y(x))\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 378

\(x^2 \left (1-x^2\right ) y'(x)=y(x) \left (x-3 x^3 y(x)\right )\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 379

\(x \left (1-2 x^3\right ) y'(x)=2 \left (1-x^3\right ) y(x)\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 380

\(\left (y'(x)+y(x)^2\right ) \left (a+b x+c x^2\right )^2+A=0\)

[_rational, _Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 381

\(x^5 y'(x)=1-3 x^4 y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 382

\(x \left (1-x^4\right ) y'(x)=\left (1-x^4\right ) y(x)+2 x \left (x^2-y(x)^2\right )\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 383

\(x^7 y'(x)+5 x^3 y(x)^2+2 \left (x^2+1\right ) y(x)^3=0\)

[_rational, _Abel]

Solution method Abel ODE, First kind

Maple
Mathematica

ODE 384

\(x^n y'(x)=a+b x^{n-1} y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 385

\(x^n y'(x)=x^{2 n-1}-y(x)^2\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 386

\(y(x) \left (x^{n-1}+y(x)\right )+x^n y'(x)+x^2=0\)

[_Riccati]

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 387

\((1-n) x^{n-1}+x^{2 n-2}+x^n y'(x)+y(x)^2=0\)

[_Riccati]

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 388

\(x^n y'(x)=a^2 x^{2 n-2}+b^2 y(x)^2\)

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

Solution method Riccati ODE, Generalized ODE

Maple
Mathematica

ODE 389

\(x^n y'(x)=x^{n-1} \left (a x^{2 n}-b y(x)^2+n y(x)\right )\)

[_rational, _Riccati]

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 390

\(x^{2 n} y'(x)=-n x^{n-1}+x^n y(x) \left (x^{2 n} y(x)^2-3 x^n y(x)+1\right )+1\)

[_Abel]

Solution method Abel ODE, First kind

Maple
Mathematica

ODE 391

\(x^k y'(x)=a x^m+b y(x)^n\)

[_Chini]

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 392

\(\sqrt {x^2+1} y'(x)=2 x-y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 393

\(\sqrt {1-x^2} y'(x)=y(x)^2+1\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 394

\(\left (x-\sqrt {x^2+1}\right ) y'(x)=y(x)+\sqrt {y(x)^2+1}\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 395

\(\sqrt {a^2+x^2} y'(x)+y(x)+x=\sqrt {a^2+x^2}\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 396

\(\sqrt {b^2+x^2} y'(x)=\sqrt {a^2+y(x)^2}\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 397

\(\sqrt {b^2-x^2} y'(x)=\sqrt {a^2-y(x)^2}\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 398

\(x \sqrt {a^2+x^2} y'(x)=y(x) \sqrt {b^2+y(x)^2}\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 399

\(x \sqrt {x^2-a^2} y'(x)=y(x) \sqrt {y(x)^2-b^2}\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 400

\(\sqrt {X} y'(x)+\sqrt {Y}=0\)

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 401

\(\sqrt {X} y'(x)=\sqrt {Y}\)

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 402

\(x^{3/2} y'(x)=a+b x^{3/2} y(x)^2\)

[_rational, [_Riccati, _special]]

Solution method Abel ODE, First kind

Maple
Mathematica

ODE 403

\(\sqrt {x^3+1} y'(x)=\sqrt {y(x)^3+1}\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 404

\(\sqrt {(1-x) x (1-a x)} y'(x)=\sqrt {(1-y(x)) y(x) (1-a y(x))}\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 405

\(\sqrt {1-x^4} y'(x)=\sqrt {1-y(x)^4}\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 406

\(\sqrt {x^4+x^2+1} y'(x)=\sqrt {y(x)^4+y(x)^2+1}\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 407

\(\sqrt {X} y'(x)=0\)

[_quadrature]

Solution method Separable ODE, Dependent variable missing

Maple
Mathematica

ODE 408

\(\sqrt {X} y'(x)+\sqrt {Y}=0\)

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 409

\(\sqrt {X} y'(x)=\sqrt {Y}\)

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 410

\(\left (x^3+1\right )^{2/3} y'(x)+\left (y(x)^3+1\right )^{2/3}=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 411

\(\left (\text {a0}+\text {a1} x+4 x^3\right )^{2/3} y'(x)+\left (\text {a0}+\text {a1} y(x)+4 y(x)^3\right )^{2/3}=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 412

\(X^{2/3} y'(x)=Y^{2/3}\)

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 413

\(\left (a+\cos ^2\left (\frac {x}{2}\right )\right ) y'(x)=y(x) \tan \left (\frac {x}{2}\right ) \left (a-y(x)+\cos ^2\left (\frac {x}{2}\right )+1\right )\)

[_Bernoulli]

Solution method Change of Variable, Two new variables

Maple
Mathematica

ODE 414

\(\left (1-4 \cos ^2(x)\right ) y'(x)=y(x) \left (4 \cos ^2(x)+1\right ) \tan (x)\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 415

\((1-\sin (x)) y'(x)+y(x) \cos (x)=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 416

\(y'(x) (\cos (x)-\sin (x))+y(x) (\sin (x)+\cos (x))=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 417

\(y'(x) \left (\text {a0}+\text {a1} \sin ^2(x)\right )+\text {a2} x \left (\text {a1} \sin ^2(x)+\text {a3}\right )+\text {a1} y(x) \sin (2 x)=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 418

\(\left (x-e^x\right ) y'(x)+\left (1-e^x\right ) y(x)+e^x x=0\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 419

\(x \log (x) y'(x)=a x (\log (x)+1)-y(x)\)

[_linear]

Solution method Linear ODE

Maple
Mathematica

ODE 420

\(y(x) y'(x)+x=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 421

\(e^{x^2} x+y(x) y'(x)=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 422

\(x^3+y(x) y'(x)+y(x)=0\)

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

Solution method Abel ODE, Second kind

Maple
Mathematica

ODE 423

\(a x+b y(x)+y(x) y'(x)=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 424

\(y(x) y'(x)+e^{-x} x (y(x)+1)=0\)

[_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

\(y(x) y'(x)+y(x)^2+4 x (x+1)=0\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 427

\(y(x) y'(x)=a x+b y(x)^2\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 428

\(y(x) y'(x)=a y(x)^2+b \cos (c+x)\)

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 429

\(y(x) y'(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2\)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica

ODE 430

\(y(x) y'(x)=a x+b x y(x)^2\)

[_separable]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 431

\(y(x) y'(x)=\csc ^2(x)-y(x)^2 \cot (x)\)

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 432

\(y(x) y'(x)=\sqrt {a^2+y(x)^2}\)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica

ODE 433

\(y(x) y'(x)=\sqrt {y(x)^2-a^2}\)

[_quadrature]

Solution method Separable ODE, Independent variable missing

Maple
Mathematica

ODE 434

\(g(x) f\left (x^2+y(x)^2\right )+y(x) y'(x)+x=0\)

[NONE]

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 435

\((y(x)+1) y'(x)=y(x)+x\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 436

\((y(x)+1) y'(x)=x^2 (1-y(x))\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 437

\((y(x)+x) y'(x)+y(x)=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 438

\((x-y(x)) y'(x)=y(x)\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 439

\((y(x)+x) y'(x)-y(x)+x=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 440

\((y(x)+x) y'(x)=x-y(x)\)

[[_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

\((x-y(x)) y'(x)=y(x) (2 x y(x)+1)\)

[[_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

\((x-y(x)) y'(x)=\left (e^{-\frac {x}{y(x)}}+1\right ) y(x)\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 445

\((y(x)+x+1) y'(x)+3 y(x)+4 x+1=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

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, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 447

\((-y(x)-x+3) y'(x)=-3 y(x)+x+1\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 448

\((y(x)-x+3) y'(x)=3 y(x)-4 x+11\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 449

\((y(x)+2 x) y'(x)-2 y(x)+x=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 450

\((-y(x)+2 x+2) y'(x)+3 (-y(x)+2 x+1)=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 451

\((-y(x)+2 x+3) y'(x)+2=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 452

\((-y(x)+2 x+4) y'(x)-2 y(x)+x+5=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 453

\((-y(x)-2 x+5) y'(x)-2 y(x)-x+4=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 454

\((y(x)-3 x+1) y'(x)=2 (x-y(x))\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 455

\((y(x)-3 x+2) y'(x)-3 y(x)-2 x+5=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 456

\((4 x-y(x)) y'(x)-5 y(x)+2 x=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 457

\((-y(x)-4 x+6) y'(x)=2 x-y(x)\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 458

\((-y(x)+5 x+1) y'(x)-5 y(x)+x+5=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 459

\(y'(x) (a+b x+y(x))+a-b x-y(x)=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 460

\(\left (x^2-y(x)\right ) y'(x)+x=0\)

[_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

\(\left (x^2-y(x)\right ) y'(x)=4 x y(x)\)

[[_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

\(x^2+2 y(x) y'(x)+y(x)^2+2 x=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 464

\(2 y(x) y'(x)=x^3+x y(x)^2\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 465

\((x-2 y(x)) y'(x)=y(x)\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 466

\((2 y(x)+x) y'(x)-y(x)+2 x=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 467

\((x-2 y(x)) y'(x)+y(x)+2 x=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 468

\((-2 y(x)+x+1) y'(x)=-y(x)+2 x+1\)

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

Solution method Exact equation

Maple
Mathematica

ODE 469

\((2 y(x)+x+1) y'(x)-2 y(x)-x+1=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 470

\((2 y(x)+x+1) y'(x)-4 y(x)+x+7=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 471

\(x^2+2 (y(x)+x) y'(x)+2 y(x)=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 472

\((-2 y(x)+2 x+3) y'(x)=-2 y(x)+6 x+1\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 473

\((-2 y(x)-4 x+1) y'(x)+y(x)+2 x=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 474

\((6 x-2 y(x)) y'(x)=-y(x)+3 x+2\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 475

\((2 y(x)+9 x+19) y'(x)-6 y(x)-2 x+18=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 476

\(\left (x^3+2 y(x)\right ) y'(x)=3 x (2-x y(x))\)

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

Solution method Exact equation

Maple
Mathematica

ODE 477

\(y'(x) (\tan (x) \sec (x)-2 y(x))+\sec (x) (2 y(x) \sin (x)+1)=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 478

\(\left (e^{-x} x-2 y(x)\right ) y'(x)=2 e^{-2 x} x-\left (-2 y(x)+e^{-x} x+e^{-x}\right ) y(x)\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 479

\(3 y(x) y'(x)+5 \cot (x) \cos ^2(y(x)) \cot (y(x))=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 480

\(3 (2-y(x)) y'(x)+x y(x)=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 481

\((x-3 y(x)) y'(x)-y(x)+3 x+4=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 482

\((-3 y(x)-x+4) y'(x)-3 y(x)-x+3=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 483

\((3 y(x)+2 x+2) y'(x)=-3 y(x)-2 x+1\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 484

\((-3 y(x)-2 x+5) y'(x)-3 y(x)-2 x+1=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 485

\((-3 y(x)+9 x+1) y'(x)-y(x)+3 x+2=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 486

\((4 y(x)+x) y'(x)-y(x)+4 x=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 487

\((4 y(x)+2 x+3) y'(x)=2 y(x)+x+1\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 488

\((-4 y(x)+2 x+5) y'(x)=-2 y(x)+x+3\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 489

\((-4 y(x)+3 x+5) y'(x)=-3 y(x)+7 x+2\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

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, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 491

\((-4 y(x)-11 x+11) y'(x)=-25 y(x)-8 x+62\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 492

\((5 y(x)+3 x+6) y'(x)=7 y(x)+x+2\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 493

\((5 y(x)+7 x) y'(x)+8 y(x)+10 x=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 494

\(\left (4 x^3+5 y(x)+x\right ) y'(x)+7 x^3+3 x^2 y(x)+4 y(x)=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 495

\((6 y(x)-x+5) y'(x)=4 y(x)-x+3\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 496

\(3 (2 y(x)+x) y'(x)=-2 y(x)-x+1\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 497

\((7 y(x)-3 x+3) y'(x)+3 y(x)-7 x+7=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 498

\((9 y(x)+x+1) y'(x)+5 y(x)+x+1=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 499

\((-12 y(x)+5 x+8) y'(x)=-5 y(x)+2 x+3\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 500

\((-16 y(x)+7 x+140) y'(x)+y(x)+8 x+25=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 501

\((21 y(x)+9 x+3) y'(x)=-5 y(x)+7 x+45\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 502

\(y'(x) (a x+b y(x))+x=0\)

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

Solution method Change of Variable, new independent variable

Maple
Mathematica

ODE 503

\(y'(x) (a x+b y(x))+y(x)=0\)

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

Solution method Change of Variable, new independent variable

Maple
Mathematica

ODE 504

\(y'(x) (a x+b y(x))+a y(x)+b x=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 505

\(y'(x) (a x+b y(x))=a y(x)+b x\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 506

\(\text {a1}+y'(x) (\text {a2}+b x+\text {c2} y(x))+b y(x)+\text {b1} x=0\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 507

\(y'(x) (\text {a2}+\text {b2} y(x)+\text {c2} y(x))=\text {a1}+\text {b1} x+\text {c1} y(x)\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 508

\(x y(x) y'(x)+y(x)^2+1=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 509

\(x y(x) y'(x)=y(x)^2+x\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 510

\(x^2+x y(x) y'(x)+y(x)^2=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 511

\(x^4+x y(x) y'(x)-y(x)^2=0\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 512

\(x y(x) y'(x)=a x^3 \cos (x)+y(x)^2\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 513

\(x y(x) y'(x)=x^2-x y(x)+y(x)^2\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 514

\(2 x^2+x y(x) y'(x)-2 x y(x)-y(x)^2=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 515

\(x y(x) y'(x)=a+b y(x)^2\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 516

\(x y(x) y'(x)=a x^n+b y(x)^2\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 517

\(x y(x) y'(x)=\left (x^2+1\right ) \left (1-y(x)^2\right )\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 518

\(x^2 \cot ^{-1}\left (\frac {y(x)}{x}\right )+x y(x) y'(x)-y(x)^2=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 519

\(x^2 e^{-\frac {2 y(x)}{x}}+x y(x) y'(x)-y(x)^2=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 520

\((x y(x)+1) y'(x)+y(x)^2=0\)

[[_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

\(a x+x (y(x)+2) y'(x)=0\)

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 525

\((x (-y(x))+3 x+2) y'(x)+y(x)=0\)

[_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

\(x (y(x)+4) y'(x)=y(x)^2+2 y(x)+2 x\)

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

Solution method Homogeneous equation, special

Maple
Mathematica

ODE 527

\(x (a+y(x)) y'(x)+b x+c y(x)=0\)

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

Solution method Change of Variable, new independent variable

Maple
Mathematica

ODE 528

\(x (a+y(x)) y'(x)=y(x) (A+B x)\)

[_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

\(x (y(x)+x) y'(x)=x^2+y(x)^2\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 532

\(2 x^2+x (x-y(x)) y'(x)+3 x y(x)-y(x)^2=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 533

\(x \sqrt {x^2-y(x)^2}+x (y(x)+x) y'(x)-y(x) (y(x)+x)=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 534

\((a+x (y(x)+x)) y'(x)=b y(x) (y(x)+x)\)

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

Solution method Homogeneous equation, special

Maple
Mathematica

ODE 535

\(x (y(x)+2 x) y'(x)=x^2+x y(x)-y(x)^2\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 536

\(4 x^2+x (4 x-y(x)) y'(x)-6 x y(x)-y(x)^2=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 537

\(x \left (x^3+y(x)\right ) y'(x)=\left (x^3-y(x)\right ) y(x)\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 538

\(x \left (2 x^3+y(x)\right ) y'(x)=\left (2 x^3-y(x)\right ) y(x)\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 539

\(x \left (2 x^3+y(x)\right ) y'(x)=6 y(x)^2\)

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

Solution method Change of Variable, new independent variable

Maple
Mathematica

ODE 540

\((1-x) y(x) y'(x)+x (1-y(x))=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 541

\((a+x) (b+x) y'(x)=x y(x)\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 542

\(-2 x^3+2 x y(x) y'(x)-y(x)^2+1=0\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 543

\(a+2 x y(x) y'(x)+y(x)^2=0\)

[_separable]

Solution method Exact equation

Maple
Mathematica

ODE 544

\(2 x y(x) y'(x)=a x+y(x)^2\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 545

\(x^2+2 x y(x) y'(x)+y(x)^2=0\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 546

\(2 x y(x) y'(x)=x^2+y(x)^2\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 547

\(2 x y(x) y'(x)=4 (2 x+1) x^2+y(x)^2\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 548

\(x^2 \left (a x^3+1\right )+2 x y(x) y'(x)=6 y(x)^2\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 549

\(3 x^2+(2 x y(x)-x+3) y'(x)+y(x)^2-y(x)=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 550

\(x (x-2 y(x)) y'(x)+y(x)^2=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 551

\(x (2 y(x)+x) y'(x)+(2 x-y(x)) y(x)=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 552

\(x (x-2 y(x)) y'(x)+(2 x-y(x)) y(x)=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 553

\(x (-2 y(x)+x+1) y'(x)+y(x) (y(x)-2 x+1)=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 554

\(x (-2 y(x)-x+1) y'(x)+y(x) (y(x)+2 x+1)=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 555

\(2 x \left (2 x^2+y(x)\right ) y'(x)+y(x) \left (12 x^2+y(x)\right )=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 556

\(-3 x^2+2 (x+1) y(x) y'(x)+y(x)^2+2 x=0\)

[_exact, _rational, _Bernoulli]

Solution method Exact equation

Maple
Mathematica

ODE 557

\(x (3 y(x)+2 x) y'(x)=y(x)^2\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 558

\(x (3 y(x)+2 x) y'(x)+3 (y(x)+x)^2=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 559

\(\left (x^2+6 x y(x)+3\right ) y'(x)+3 y(x)^2+2 x y(x)+2 x=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 560

\(x^3+3 x (2 y(x)+x) y'(x)+3 y(x) (y(x)+2 x)=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 561

\(a x y(x) y'(x)=x^2+y(x)^2\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 562

\(a x y(x) y'(x)+x^2-y(x)^2=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 563

\(x y'(x) (a+b y(x))=c y(x)\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 564

\(x (x-a y(x)) y'(x)=y(x) (y(x)-a x)\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 565

\(y'(x) (x (A x+B y(x))+\text {a0}+\text {a1} x+\text {a2} y(x))=y(x) (A x+B y(x))+\text {b0}+\text {b1} x+\text {b2} y(x)\)

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

Solution method Homogeneous equation, Jacobi equation

Maple
Mathematica

ODE 566

\(y'(x) (x (\text {a1}+\text {b2} x+\text {c2} y(x))+\text {a1}+\text {b1} x+\text {c1} y(x))=y(x) (\text {a2}+\text {b2} x+\text {c2} y(x))+\text {a3}+\text {b3} x+\text {c2} y(x)\)

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

Solution method Homogeneous equation, Jacobi equation

Maple
Mathematica

ODE 567

\(x y'(x) \left (a y(x)+x^n\right )+y(x)^2 (b+c y(x))=0\)

[_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

\(\left (1-x^2 y(x)\right ) y'(x)-x y(x)^2+1=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 569

\(\left (1-x^2 y(x)\right ) y'(x)+x y(x)^2-1=0\)

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

Solution method Homogeneous equation, special

Maple
Mathematica

ODE 570

\(x (1-x y(x)) y'(x)+y(x) (x y(x)+1)=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 571

\(x (x y(x)+2) y'(x)=2 x^3-x y(x)^2-2 y(x)+3\)

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

Solution method Exact equation

Maple
Mathematica

ODE 572

\(x (2-x y(x)) y'(x)-x (x y(x)+1) y(x)^2+2 y(x)=0\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 573

\(x (3-x y(x)) y'(x)=y(x) (x y(x)-1)\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 574

\(x^2 (1-y(x)) y'(x)+(1-x) y(x)=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 575

\(x^2 (1-y(x)) y'(x)+(x+1) y(x)^2=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 576

\(\left (x^2+1\right ) y(x) y'(x)+x \left (1-y(x)^2\right )=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 577

\(\left (1-x^2\right ) y(x) y'(x)+2 x^2+x y(x)^2=0\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 578

\(2 x^2 y(x) y'(x)=x^2 (2 x+1)-y(x)^2\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 579

\(x (1-2 x y(x)) y'(x)+y(x) (2 x y(x)+1)=0\)

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

Solution method Change of Variable, Two new variables

Maple
Mathematica

ODE 580

\(x (2 x y(x)+1) y'(x)+y(x) (3 x y(x)+2)=0\)

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

Solution method Homogeneous equation, isobaric equation

Maple
Mathematica

ODE 581

\(y(x) \left (-x^2 y(x)^2+2 x y(x)+1\right )+x (2 x y(x)+1) y'(x)=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 582

\(x^2 (x-2 y(x)) y'(x)=2 x^3-4 x y(x)^2+y(x)^3\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 583

\(2 x (x+1) y(x) y'(x)=y(x)^2+1\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 584

\(3 x^2 y(x) y'(x)+2 x y(x)^2+1=0\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 585

\(x^2 (4 x-3 y(x)) y'(x)=y(x) \left (6 x^2-3 x y(x)+2 y(x)^2\right )\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 586

\(\left (1-x^3 y(x)\right ) y'(x)=x^2 y(x)^2\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 587

\(a+2 x^3 y(x) y'(x)+3 x^2 y(x)^2=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 588

\(x \left (3-2 x^2 y(x)\right ) y'(x)=3 x^2 y(x)^2-3 y(x)+4 x\)

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

Solution method Exact equation

Maple
Mathematica

ODE 589

\(x \left (2 x^2 y(x)+3\right ) y'(x)+y(x) \left (3 x^2 y(x)+4\right )=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 590

\(3 x^4+8 x^3 y(x) y'(x)-6 x^2 y(x)^2-y(x)^4=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 591

\(x y(x) \left (a+b x^2\right ) y'(x)=A+B y(x)^2\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 592

\(3 x^4 y(x) y'(x)=1-2 x^3 y(x)^2\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 593

\(x^7 y(x) y'(x)=5 x^3 y(x)+2 \left (x^2+1\right )\)

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

Solution method Abel ODE, Second kind

Maple
Mathematica

ODE 594

\(\sqrt {x^2+1} y(x) y'(x)+x \sqrt {y(x)^2+1}=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 595

\(\sqrt {x^2+1} (y(x)+1) y'(x)=y(x)^3\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 596

\(y'(x) (\text {g0}(x)+\text {g1}(x) y(x))=\text {f0}(x)+\text {f1}(x) y(x)+\text {f2}(x) y(x)^2+\text {f3}(x) y(x)^3\)

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

Solution method Abel ODE, Second kind

Maple
Mathematica

ODE 597

\(y(x)^2 y'(x)+x (2-y(x))=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 598

\(y(x)^2 y'(x)=x \left (y(x)^2+1\right )\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 599

\(\left (y(x)^2+x\right ) y'(x)+y(x)=a+b x\)

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica

ODE 600

\(\left (x-y(x)^2\right ) y'(x)=x^2-y(x)\)

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica

ODE 601

\(\left (x^2+y(x)^2\right ) y'(x)+x y(x)=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 602

\(\left (x^2+y(x)^2\right ) y'(x)=x y(x)\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 603

\(\left (x^2-y(x)^2\right ) y'(x)=2 x y(x)\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 604

\(\left (x^2-y(x)^2\right ) y'(x)+x (2 y(x)+x)=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 605

\(\left (x^2+y(x)^2\right ) y'(x)+2 x (y(x)+2 x)=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 606

\(\left (-x^2+y(x)^2+1\right ) y'(x)=x^2-y(x)^2+1\)

[[_1st_order, _with_linear_symmetries], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 607

\(\left (a^2+x^2+y(x)^2\right ) y'(x)+2 x y(x)=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 608

\(\left (a^2+x^2+y(x)^2\right ) y'(x)+b^2+x^2+2 x y(x)=0\)

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica

ODE 609

\(\left (x^2+y(x)^2+x\right ) y'(x)=y(x)\)

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 610

\(\left (3 x^2-y(x)^2\right ) y'(x)=2 x y(x)\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 611

\(\left (x^4+y(x)^2\right ) y'(x)=4 x^3 y(x)\)

[[_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

\(\left (y(x)^2+2 y(x)+x\right ) y'(x)+y(x)^2 (y(x)+x)^2+y(x) (y(x)+1)=0\)

[_rational]

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 614

\(\left (x^2+y(x)^2+2 y(x)\right ) y'(x)+2 x=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 615

\(\left (x^3-y(x)^2+2 y(x)\right ) y'(x)+3 x^2 y(x)=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 616

\(\left (y(x)^2+x y(x)+y(x)+1\right ) y'(x)+y(x)+1=0\)

[[_1st_order, _with_linear_symmetries], _rational]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 617

\((y(x)+x)^2 y'(x)=a^2\)

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

Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\)

Maple
Mathematica

ODE 618

\((x-y(x))^2 y'(x)=a^2\)

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

Solution method Equation linear in the variables, \(y'(x)=f(a+b x+ c y(x))\)

Maple
Mathematica

ODE 619

\(\left (x^2+2 x y(x)-y(x)^2\right ) y'(x)+x^2-2 x y(x)+y(x)^2=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 620

\((x-y(x))^2 y'(x)=(-y(x)+x+1)^2\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 621

\((y(x)+x)^2 y'(x)=(y(x)+x+2)^2\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 622

\((y(x)+x)^2 y'(x)=x^2-2 x y(x)+5 y(x)^2\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 623

\(y'(x) (a+b+y(x)+x)^2=2 (a+y(x))^2\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 624

\(\left (2 x^2+4 x y(x)-y(x)^2\right ) y'(x)=x^2-4 x y(x)-2 y(x)^2\)

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

Solution method Exact equation

Maple
Mathematica

ODE 625

\((y(x)+3 x)^2 y'(x)=4 y(x) (2 y(x)+3 x)\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 626

\((-y(x)-3 x+1)^2 y'(x)=(-4 y(x)-6 x+3) (1-2 y(x))\)

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

Solution method Change of Variable, Two new variables

Maple
Mathematica

ODE 627

\(y'(x) \left (\cot (x)-2 y(x)^2\right )=y(x)^3 \csc (x) \sec (x)\)

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

Solution method Change of Variable, new independent variable

Maple
Mathematica

ODE 628

\(3 y(x)^2 y'(x)=a y(x)^3+x+1\)

[_rational, _Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 629

\(\left (x^2-3 y(x)^2\right ) y'(x)+2 x y(x)+1=0\)

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica

ODE 630

\(\left (2 x^2+3 y(x)^2\right ) y'(x)+x (y(x)+3 x)=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 631

\(3 \left (x^2-y(x)^2\right ) y'(x)-2 y(x)^3+6 x (x+1) y(x)+3 e^x=0\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 632

\(\left (3 x^2+2 x y(x)+4 y(x)^2\right ) y'(x)+2 x^2+6 x y(x)+y(x)^2=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 633

\((2 y(x)-3 x+1)^2 y'(x)=(-3 y(x)+2 x+4)^2\)

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

Solution method Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Maple
Mathematica

ODE 634

\(\left (-3 x^2 y(x)+6 y(x)^2+1\right ) y'(x)+x^2-3 x y(x)^2=0\)

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica

ODE 635

\(a+(x-6 y(x))^2 y'(x)-6 y(x)^2+2 x y(x)=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 636

\(\left (a y(x)^2+x^2\right ) y'(x)=x y(x)\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 637

\(\left (a y(x)^2+x^2+x y(x)\right ) y'(x)=a x^2+x y(x)+y(x)^2\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 638

\(\left (a x^2-a y(x)^2+2 x y(x)\right ) y'(x)-2 a x y(x)+x^2-y(x)^2=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 639

\(y'(x) \left (x^2 (a+2 b)+2 x (2 b+c) y(x)+3 c y(x)^2\right )+2 x (a+2 b) y(x)+3 a x^2+(2 b+c) y(x)^2=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 640

\(y'(x) \left (a x^2+2 b x y(x)+c y(x)^2\right )+2 a x y(x)+b y(x)^2+k x^2=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 641

\(x \left (1-y(x)^2\right ) y'(x)=\left (x^2+1\right ) y(x)\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 642

\(x \left (3 x-y(x)^2\right ) y'(x)+y(x) \left (5 x-2 y(x)^2\right )=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 643

\(x \left (x^2+y(x)^2\right ) y'(x)=y(x) \left (x^4+x^2+y(x)^2\right )\)

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

Solution method Homogeneous equation, \(xy'(x)=x f(x) g(u)+y(x)\)

Maple
Mathematica

ODE 644

\(x \left (-x^2+y(x)^2+1\right ) y'(x)+y(x) \left (x^2-y(x)^2+1\right )=0\)

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

Solution method Homogeneous equation, special

Maple
Mathematica

ODE 645

\(x \left (a-x^2-y(x)^2\right ) y'(x)+y(x) \left (a+x^2+y(x)^2\right )=0\)

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

Solution method Homogeneous equation, special

Maple
Mathematica

ODE 646

\(x \left (2 x^2+y(x)^2\right ) y'(x)=y(x) \left (2 x^2+3 y(x)^2\right )\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 647

\(\left (x \left (a-x^2-y(x)^2\right )+y(x)\right ) y'(x)-y(x) \left (a-x^2-y(x)^2\right )+x=0\)

[[_1st_order, _with_linear_symmetries], _rational]

Solution method Change of Variable, Two new variables

Maple
Mathematica

ODE 648

\(x (a+y(x))^2 y'(x)=b y(x)^2\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 649

\(x \left (x^2-x y(x)+y(x)^2\right ) y'(x)+y(x) \left (x^2+x y(x)+y(x)^2\right )=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 650

\(x \left (x^2-x y(x)-y(x)^2\right ) y'(x)=y(x) \left (x^2+x y(x)-y(x)^2\right )\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 651

\(x \left (a x y(x)+x^2+y(x)^2\right ) y'(x)=y(x) \left (b x y(x)+x^2+y(x)^2\right )\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 652

\(x \left (x^2-2 y(x)^2\right ) y'(x)=y(x) \left (2 x^2-y(x)^2\right )\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 653

\(x \left (x^2+2 y(x)^2\right ) y'(x)=y(x) \left (2 x^2+3 y(x)^2\right )\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 654

\(2 x \left (5 x^2+y(x)^2\right ) y'(x)=x^2 y(x)-y(x)^3\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 655

\(x \left (a x y(x)+x^2+2 y(x)^2\right ) y'(x)=y(x)^2 (a x+2 y(x))\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 656

\(3 x y(x)^2 y'(x)=2 x-y(x)^3\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 657

\(\left (3 x y(x)^2-4 x+1\right ) y'(x)=y(x) \left (2-y(x)^2\right )\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 658

\(x \left (x-3 y(x)^2\right ) y'(x)+y(x) \left (2 x-y(x)^2\right )=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 659

\(x^3+3 x \left (y(x)^2+x\right ) y'(x)-3 x y(x)-2 y(x)^3=0\)

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 660

\(x \left (-3 x^3 y(x)+x^3+4 y(x)^2\right ) y'(x)=6 y(x)^3\)

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

Solution method Change of Variable, new independent variable

Maple
Mathematica

ODE 661

\(6 x y(x)^2 y'(x)+2 y(x)^3+x=0\)

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

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 662

\(x \left (6 y(x)^2+x\right ) y'(x)-3 y(x)^3+x y(x)=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 663

\(x \left (x^2-6 y(x)^2\right ) y'(x)=4 y(x) \left (x^2+3 y(x)^2\right )\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 664

\(x \left (3 x-7 y(x)^2\right ) y'(x)+y(x) \left (5 x-3 y(x)^2\right )=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 665

\(x^3+x^2 y(x)^2 y'(x)-x+1=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 666

\(\left (1-x^2 y(x)^2\right ) y'(x)=x y(x)^3\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 667

\(\left (1-x^2 y(x)^2\right ) y'(x)=y(x)^2 (x y(x)+1)\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 668

\(x \left (x y(x)^2+1\right ) y'(x)+y(x)=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 669

\(x \left (x y(x)^2+1\right ) y'(x)=y(x) \left (2-3 x y(x)^2\right )\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 670

\(x^2 (a+y(x))^2 y'(x)=\left (x^2+1\right ) \left (a^2+y(x)^2\right )\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 671

\(\left (x^2+1\right ) \left (y(x)^2+1\right ) y'(x)+2 x y(x) \left (1-y(x)^2\right )=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 672

\(\left (x^2+1\right ) \left (y(x)^2+1\right ) y'(x)+2 x y(x) (1-y(x))^2=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 673

\(\left (-x^3+6 x^2 y(x)^2+1\right ) y'(x)=x \left (-4 y(x)^3+3 x y(x)+6\right )\)

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica

ODE 674

\(x \left (4 x^2 y(x)-12 x y(x)^2+5 x+3\right ) y'(x)+y(x) \left (6 x^2 y(x)-8 x y(x)^2+10 x+3\right )=0\)

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica

ODE 675

\(x^3 \left (y(x)^2+1\right ) y'(x)+3 x^2 y(x)=0\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 676

\(y(x) \left (x^2 y(x)^2+1\right )+x (1-x y(x))^2 y'(x)=0\)

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

Solution method Homogeneous equation, isobaric equation

Maple
Mathematica

ODE 677

\(\left (1-x^4 y(x)^2\right ) y'(x)=x^3 y(x)^3\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 678

\(\left (3 x-y(x)^3\right ) y'(x)=x^2-3 y(x)\)

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica

ODE 679

\(\left (x^3-y(x)^3\right ) y'(x)+x^2 y(x)=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 680

\(x^2 (a x+3 y(x))+\left (x^3+y(x)^3\right ) y'(x)=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 681

\(\left (-x^2 y(x)-y(x)^3+x\right ) y'(x)=x^3+x y(x)^2-y(x)\)

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica

ODE 682

\(\left (a^2 x+y(x) \left (x^2-y(x)^2\right )\right ) y'(x)+x \left (x^2-y(x)^2\right )=a^2 y(x)\)

[_rational]

Solution method Change of Variable, Two new variables

Maple
Mathematica

ODE 683

\(y(x) \left (a+x^2+y(x)^2\right ) y'(x)=x \left (a-x^2-y(x)^2\right )\)

[_exact, _rational]

Solution method Exact equation

Maple
Mathematica

ODE 684

\(y(x) \left (3 x^2+y(x)^2\right ) y'(x)+x \left (x^2+3 y(x)^2\right )=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 685

\(y(x) \left (a-3 x^2-y(x)^2\right ) y'(x)+x \left (a-x^2+y(x)^2\right )=0\)

[_rational]

Solution method Change of Variable, Two new variables

Maple
Mathematica

ODE 686

\(2 y(x)^3 y'(x)=x^3-x y(x)^2\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 687

\(y(x) \left (2 y(x)^2+1\right ) y'(x)=x \left (2 x^2+1\right )\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 688

\(x^3+y(x) \left (3 x^2+2 y(x)^2\right ) y'(x)=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 689

\(y(x) \left (5 x^2+2 y(x)^2\right ) y'(x)+x \left (x^2+5 y(x)^2\right )=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 690

\(2 x^3+3 x^2 y(x)+\left (-x^3+x^2+3 x y(x)^2+2 y(x)^3\right ) y'(x)-y(x)^3+y(x)^2=0\)

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 691

\(4 x^3+9 x^2 y(x)+\left (3 x^3+6 x^2 y(x)-3 x y(x)^2+20 y(x)^3\right ) y'(x)+6 x y(x)^2-y(x)^3=0\)

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

Solution method Exact equation

Maple
Mathematica

ODE 692

\(\left (a y(x)^3+x^3\right ) y'(x)=x^2 y(x)\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 693

\(y'(x) \left (a x^2-b x^3+3 c x y(x)^2+2 c y(x)^3\right )+a y(x)^2+2 b x^3+3 b x^2 y(x)-c y(x)^3=0\)

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 694

\(x y(x)^3 y'(x)=\left (1-x^2\right ) \left (y(x)^2+1\right )\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 695

\(x \left (x-y(x)^3\right ) y'(x)=y(x) \left (y(x)^3+3 x\right )\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 696

\(x \left (2 x^3+y(x)^3\right ) y'(x)=y(x) \left (2 x^3-x^2 y(x)+y(x)^3\right )\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 697

\(x \left (2 x^3-y(x)^3\right ) y'(x)=y(x) \left (x^3-2 y(x)^3\right )\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 698

\(x \left (x^3+3 x^2 y(x)+y(x)^3\right ) y'(x)=y(x)^2 \left (3 x^2+y(x)^2\right )\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 699

\(x \left (x^3-2 y(x)^3\right ) y'(x)=y(x) \left (2 x^3-y(x)^3\right )\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 700

\(x \left (x^4-2 y(x)^3\right ) y'(x)+y(x) \left (2 x^4+y(x)^3\right )=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 701

\(x \left (2 y(x)^3+y(x)+x\right ) y'(x)=(x-y(x)) y(x)\)

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 702

\(\left (-7 x y(x)^3-y(x)+5 x\right ) y'(x)-y(x)^4+5 y(x)=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 703

\(y(x) \left (1-2 x^3 y(x)\right )+x \left (1-2 x y(x)^3\right ) y'(x)=0\)

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 704

\(x \left (-2 x y(x)^3-x y(x)^2+2\right ) y'(x)+2 y(x)+1=0\)

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

Solution method Change of Variable, new independent variable

Maple
Mathematica

ODE 705

\(\left (-10 x^2 y(x)^3+3 y(x)^2+2\right ) y'(x)=x \left (5 y(x)^4+1\right )\)

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

Solution method Exact equation

Maple
Mathematica

ODE 706

\(x y'(x) \left (a+b x y(x)^3\right )+y(x) \left (a+c x^3 y(x)\right )=0\)

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 707

\(y(x) \left (1-2 x^3 y(x)^2\right )+x \left (1-2 x^2 y(x)^3\right ) y'(x)=0\)

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 708

\(x (1-x y(x)) \left (1-x^2 y(x)^2\right ) y'(x)+y(x) (x y(x)+1) \left (x^2 y(x)^2+1\right )=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 709

\(\left (x^2-y(x)^4\right ) y'(x)=x y(x)\)

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

Solution method Change of Variable, new independent variable

Maple
Mathematica

ODE 710

\(\left (x^3-y(x)^4\right ) y'(x)=3 x^2 y(x)\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 711

\(\left (a^2 x^2+\left (x^2+y(x)^2\right )^2\right ) y'(x)=a^2 x y(x)\)

[_rational]

Solution method Change of Variable, Two new variables

Maple
Mathematica

ODE 712

\(2 \left (x-y(x)^4\right ) y'(x)=y(x)\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 713

\(\left (-2 y(x)^4-x y(x)^3+4 x\right ) y'(x)=y(x) \left (y(x)^3+2\right )\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 714

\(y(x) y'(x) \left ((a x+b y(x))^3+a x^3\right )+x \left ((a x+b y(x))^3+b y(x)^3\right )=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 715

\(\left (2 x^2 y(x)^3+x y(x)^4+2 y(x)+x\right ) y'(x)+y(x) \left (y(x)^4+1\right )=0\)

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 716

\(2 x \left (x^3+y(x)^4\right ) y'(x)=y(x) \left (x^3+2 y(x)^4\right )\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 717

\(x \left (1-x^2 y(x)^4\right ) y'(x)+y(x)=0\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 718

\(\left (x^2-y(x)^5\right ) y'(x)=2 x y(x)\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 719

\(x \left (x^3+y(x)^5\right ) y'(x)=y(x) \left (x^3-y(x)^5\right )\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 720

\(y(x)^3 \left (3 x^5 y(x)^5-1\right )+x^3 \left (5 x^3 y(x)^7+1\right ) y'(x)=0\)

[_rational]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 721

\(y'(x) (\text {f1}(x,y(x))+x \text {f2}(x,y(x)))=y(x) \text {f2}(x,y(x))+\text {f3}(x,y(x))\)

[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

\(x y'(x) \left (a+x y(x)^n\right )+b y(x)=0\)

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

Solution method Change of Variable, new independent variable

Maple
Mathematica

ODE 724

\(f(x) y(x)^m y'(x)+g(x) y(x)^{m+1}+h(x) y(x)^n=0\)

[_Bernoulli]

Solution method The Bernoulli ODE

Maple
Mathematica

ODE 725

\(\sqrt {b^2+y(x)^2} y'(x)=\sqrt {a^2+x^2}\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 726

\(\sqrt {b^2-y(x)^2} y'(x)=\sqrt {a^2-x^2}\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 727

\(\sqrt {Y} y'(x)=\sqrt {X}\)

[_quadrature]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 728

\(\left (\sqrt {y(x)+x}+1\right ) y'(x)+1=0\)

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

Solution method Change of Variable, new dependent variable

Maple
Mathematica

ODE 729

\(\sqrt {x y(x)} y'(x)-y(x)+x=\sqrt {x y(x)}\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 730

\(\left (x-2 \sqrt {x y(x)}\right ) y'(x)=y(x)\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 731

\(\left (x^2+1\right )^{3/2} \left (y(x)+\sqrt {y(x)^2+1}\right ) y'(x)=y(x)^2+1\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 732

\(\left (x^2+1\right )^{3/2} \left (y(x)+\sqrt {y(x)^2+1}\right ) y'(x)=y(x)^2+1\)

[_separable]

Solution method Separable ODE, Neither variable missing

Maple
Mathematica

ODE 733

\(\left (x-\sqrt {x^2+y(x)^2}\right ) y'(x)=y(x)\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 734

\(x \left (1-\sqrt {x^2-y(x)^2}\right ) y'(x)=y(x)\)

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

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 735

\(x \left (\sqrt {x^2+y(x)^2}+x\right ) y'(x)+\sqrt {x^2+y(x)^2} y(x)=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 736

\(x y(x) \left (\sqrt {x^2-y(x)^2}+x\right ) y'(x)=x y(x)^2-\left (x^2-y(x)^2\right )^{3/2}\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method Homogeneous equation

Maple
Mathematica

ODE 737

\(\left (x-y(x)^2 \sqrt {y(x)^2-x^2}\right ) y'(x)=y(x) \left (x \sqrt {y(x)^2-x^2}+1\right )\)

[NONE]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 738

\(\left (x \sqrt {x^2+y(x)^2+1}-y(x) \left (x^2+y(x)^2\right )\right ) y'(x)=\sqrt {x^2+y(x)^2+1} y(x)+x \left (x^2+y(x)^2\right )\)

[[_1st_order, _with_linear_symmetries]]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 739

\(y'(x) \left (x^2 \sec (x) \cos (y(x))+1\right )-y(x) \tan (x)+\sec (x) \sin (y(x))=0\)

[NONE]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 740

\(y'(x) \cos (y(x)) (\cos (y(x))-\sin (A) \sin (x))+\cos (x) (\cos (x)-\sin (A) \sin (y(x)))=0\)

[_exact]

Solution method Exact equation

Maple
Mathematica

ODE 741

\(y'(x) (a \cos (a y(x)+b x)-b \sin (a x+b y(x)))-a \sin (a x+b y(x))+b \cos (a y(x)+b x)=0\)

[_exact]

Solution method Exact equation

Maple
Mathematica

ODE 742

\(y'(x) (a \sin (x y(x))-\sin (y(x))+\cos (y(x)+x))+y(x) \sin (x y(x))+\cos (y(x)+x)+\cos (x)=0\)

[NONE]

Solution method Exact equation

Maple
Mathematica

ODE 743

\(y'(x) (\cos (x) \sec (y(x))+x)+\tan (y(x))-y(x) \sin (x) \sec (y(x))=0\)

[NONE]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 744

\(y'(x) \left (x^2+2 y(x) \sin (x) \sec (y(x))\right )+2 x \tan (y(x))+y(x)^2 \cos (x) \sec (y(x))=0\)

[NONE]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 745

\(y'(x) \left (x^2 \sec ^2(y(x))-6 x y(x)+2\right )-3 y(x)^2+2 x \tan (y(x))=0\)

[_exact]

Solution method Exact equation

Maple
Mathematica

ODE 746

\(y'(x) ((y(x)+x) \tan (y(x))+1)+1=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 747

\(x y'(x) \left (x-y(x) \tan \left (\frac {y(x)}{x}\right )\right )+y(x) \left (y(x) \tan \left (\frac {y(x)}{x}\right )+x\right )=0\)

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

Solution method Homogeneous equation

Maple
Mathematica

ODE 748

\(\left (x e^{y(x)}+e^x\right ) y'(x)+e^x y(x)+e^{y(x)}=0\)

[_exact]

Solution method Exact equation

Maple
Mathematica

ODE 749

\(y'(x) (-\log (y(x))-2 x+1)+2 y(x)=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method Exact equation, integrating factor

Maple
Mathematica

ODE 750

\(y'(x) (x \cosh (y(x))+\sinh (x))+\sinh (y(x))+y(x) \cosh (x)=0\)

[_exact]

Solution method Exact equation

Maple
Mathematica

ODE 751

\((\sinh (x)+1) y'(x) \sinh (y(x))+\cosh (x) (\cosh (y(x))-1)=0\)

[_separable]

Solution method Exact equation

Maple
Mathematica

ODE 752

\(y'(x)^2=a x^n\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 753

\(y'(x)^2=y(x)\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 754

\(y'(x)^2=x-y(x)\)

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

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 755

\(y'(x)^2=x^2+y(x)\)

[[_homogeneous, `class G`]]

Solution method Homogeneous ODE, The Isobaric equation

Maple
Mathematica

ODE 756

\(x^2+y'(x)^2=4 y(x)\)

[[_homogeneous, `class G`]]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 757

\(3 x^2+y'(x)^2=8 y(x)\)

[[_homogeneous, `class G`]]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 758

\(a x^2+b y(x)+y'(x)^2=0\)

[[_homogeneous, `class G`]]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 759

\(y'(x)^2=y(x)^2+1\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 760

\(y'(x)^2=1-y(x)^2\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 761

\(y'(x)^2=a^2-y(x)^2\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 762

\(y'(x)^2=a^2 y(x)^2\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 763

\(y'(x)^2=a+b y(x)^2\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 764

\(y'(x)^2=x^2 y(x)^2\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 765

\(y'(x)^2=(y(x)-1) y(x)^2\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 766

\(y'(x)^2=(y(x)-a) (y(x)-b) (y(x)-c)\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 767

\(y'(x)^2=a^2 y(x)^n\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 768

\(y'(x)^2=a^2 y(x)^2 \left (1-\log ^2(y(x))\right )\)

[_quadrature]

Solution method Change of variable

Maple
Mathematica

ODE 769

\(f(x) (y(x)-a) (y(x)-b)+y'(x)^2=0\)

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

Solution method Binomial equation \((y')^m + F(x) G(y)=0\)

Maple
Mathematica

ODE 770

\(f(x) (y(x)-a)^2 (y(x)-b)+y'(x)^2=0\)

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

Solution method Binomial equation \((y')^m + F(x) G(y)=0\)

Maple
Mathematica

ODE 771

\(f(x) (y(x)-a) (y(x)-b) (y(x)-c)+y'(x)^2=0\)

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

Solution method Binomial equation \((y')^m + F(x) G(y)=0\)

Maple
Mathematica

ODE 772

\(f(x) (y(x)-a)^2 (y(x)-b) (y(x)-c)+y'(x)^2=0\)

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

Solution method Binomial equation \((y')^m + F(x) G(y)=0\)

Maple
Mathematica

ODE 773

\(f(x) (y(x)-\text {a1}) (y(x)-\text {a2}) (y(x)-\text {a3}) (y(x)-\text {a4})+y'(x)^2=0\)

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

Solution method Binomial equation \((y')^m + F(x) G(y)=0\)

Maple
Mathematica

ODE 774

\(y'(x)^2=f(x)^2 (y(x)-a) (y(x)-b) (y(x)-c)^2\)

[_separable]

Solution method Change of variable

Maple
Mathematica

ODE 775

\(y'(x)^2=f(x)^2 (y(x)-a) (y(x)-b) (y(x)-u(x))^2\)

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

Solution method Change of variable

Maple
Mathematica

ODE 776

\(y'(x)^2+2 y'(x)+x=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 777

\(a (x-y(x))+y'(x)^2-2 y'(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 778

\(y'(x)^2-2 y'(x)-y(x)^2=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 779

\(y'(x)^2-5 y'(x)+6=0\)

[_quadrature]

Solution method Missing Variables ODE, Both independent and dependent variable missing

Maple
Mathematica

ODE 780

\(y'(x)^2-7 y'(x)+12=0\)

[_quadrature]

Solution method Missing Variables ODE, Both independent and dependent variable missing

Maple
Mathematica

ODE 781

\(a y'(x)+b+y'(x)^2=0\)

[_quadrature]

Solution method Missing Variables ODE, Both independent and dependent variable missing

Maple
Mathematica

ODE 782

\(a y'(x)+b x+y'(x)^2=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(x\)

Maple
Mathematica

ODE 783

\(a y'(x)+b y(x)+y'(x)^2=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 784

\(y'(x)^2+x y'(x)+1=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(x\)

Maple
Mathematica

ODE 785

\(y'(x)^2+x y'(x)-y(x)=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 786

\(y'(x)^2-x y'(x)+y(x)=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 787

\(y'(x)^2-x y'(x)-y(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 788

\(y'(x)^2+x y'(x)-y(x)+x=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 789

\(y'(x)^2+(1-x) y'(x)+y(x)=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 790

\(y'(x)^2-(x+1) y'(x)+y(x)=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 791

\(y'(x)^2-(2-x) y'(x)-y(x)+1=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 792

\((a+x) y'(x)+y'(x)^2-y(x)=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 793

\(y'(x)^2-2 x y'(x)+1=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(x\)

Maple
Mathematica

ODE 794

\(-3 x^2+2 x y'(x)+y'(x)^2=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 795

\(y'(x)^2+2 x y'(x)-y(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 796

\(y'(x)^2+2 x y'(x)-y(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method Change of variable

Maple
Mathematica

ODE 797

\(y'(x)^2-2 x y'(x)+2 y(x)=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 798

\(y'(x)^2-(2 x+1) y'(x)-(1-x) x=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 799

\(y'(x)^2+2 (1-x) y'(x)-2 (x-y(x))=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 800

\(y'(x)^2+3 x y'(x)-y(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 801

\(y'(x)^2-4 (x+1) y'(x)+4 y(x)=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 802

\(a x y'(x)+y'(x)^2=b c x^2\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 803

\(-a x y'(x)+a y(x)+y'(x)^2=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 804

\(a x y'(x)+b x^2+c y(x)+y'(x)^2=0\)

[[_homogeneous, `class G`]]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 805

\((a+b x) y'(x)+c+y'(x)^2=b y(x)\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 806

\(-2 x^2 y'(x)+2 x y'(x)+y'(x)^2=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 807

\(a x^2 y'(x)+b x y(x)+y'(x)^2=0\)

[[_homogeneous, `class G`]]

Solution method Homogeneous ODE, The Isobaric equation

Maple
Mathematica

ODE 808

\(a x^3 y'(x)-2 a x^2 y(x)+y'(x)^2=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method Homogeneous ODE, The Isobaric equation

Maple
Mathematica

ODE 809

\(-2 a x^3 y'(x)+4 a x^2 y(x)+y'(x)^2=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method Change of variable

Maple
Mathematica

ODE 810

\(4 x^5 y'(x)-12 x^4 y(x)+y'(x)^2=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 811

\(y'(x)^2-2 \cosh (x) y'(x)+1=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 812

\(y'(x)^2+y(x) y'(x)=x (y(x)+x)\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 813

\(y'(x)^2-y(x) y'(x)+e^x=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 814

\(y'(x)^2+(y(x)+x) y'(x)+x y(x)=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 815

\(y'(x)^2-2 y(x) y'(x)-2 x=0\)

[_dAlembert]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 816

\(y'(x)^2+(2 y(x)+1) y'(x)+(y(x)-1) y(x)=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Use new variable

Maple
Mathematica

ODE 817

\(y'(x)^2-2 (x-y(x)) y'(x)-4 x y(x)=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 818

\(y'(x)^2-(4 y(x)+1) y'(x)+y(x) (4 y(x)+1)=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 819

\(y'(x)^2-2 (1-3 y(x)) y'(x)-(4-9 y(x)) y(x)=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 820

\(y(x) (3 a+b+9 y(x))+(a+6 y(x)) y'(x)+y'(x)^2=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 821

\(a y(x) y'(x)-a x+y'(x)^2=0\)

[_dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 822

\(-a y(x) y'(x)-a x+y'(x)^2=0\)

[_dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 823

\(y'(x) (a x+b y(x))+a b x y(x)+y'(x)^2=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 824

\(y(x)^2 \log (a y(x))-x y(x) y'(x)+y'(x)^2=0\)

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

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 825

\(y'(x)^2-(2 x y(x)+1) y'(x)+2 x y(x)=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 826

\(y'(x)^2-\left (y(x)^2+4\right ) y'(x)+y(x)^2+4=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Use new variable

Maple
Mathematica

ODE 827

\(-(x-y(x)) y(x) y'(x)+y'(x)^2-x y(x)^3=0\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 828

\(x y(x)^2 y'(x)+y'(x)^2+y(x)^3=0\)

[[_homogeneous, `class G`]]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 829

\(-2 x^3 y(x)^2 y'(x)-4 x^2 y(x)^3+y'(x)^2=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method Change of variable

Maple
Mathematica

ODE 830

\(x^4 y(x)^4-x \left (x^2+y(x)^2\right ) y(x) y'(x)+y'(x)^2=0\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 831

\(2 x y(x)^3 y'(x)+y'(x)^2+y(x)^4=0\)

[[_homogeneous, `class G`]]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 832

\(y'(x)^2+2 y(x) \cot (x) y'(x)-y(x)^2=0\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 833

\(y'(x)^2-3 x y(x)^{2/3} y'(x)+9 y(x)^{5/3}=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method Change of variable

Maple
Mathematica

ODE 834

\(y'(x)^2=e^{4 x-2 y(x)} \left (y'(x)-1\right )\)

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

Solution method Change of variable

Maple
Mathematica

ODE 835

\(2 y'(x)^2+x y'(x)-2 y(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 836

\(2 y'(x)^2-(1-x) y'(x)-y(x)=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 837

\(-2 x^2 y'(x)+2 y'(x)^2+3 x y(x)=0\)

[[_homogeneous, `class G`]]

Solution method Homogeneous ODE, The Isobaric equation

Maple
Mathematica

ODE 838

\(2 y'(x)^2+2 (6 y(x)-1) y'(x)+3 y(x) (6 y(x)-1)=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 839

\(3 y'(x)^2-2 x y'(x)+y(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 840

\(x^2+4 x y'(x)+3 y'(x)^2-y(x)=0\)

[[_homogeneous, `class G`]]

Solution method Change of variable

Maple
Mathematica

ODE 841

\(4 y'(x)^2=9 x\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 842

\(4 y'(x)^2+2 x e^{-2 y(x)} y'(x)-e^{-2 y(x)}=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method Change of variable

Maple
Mathematica

ODE 843

\(4 y'(x)^2+2 e^{2 x-2 y(x)} y'(x)-e^{2 x-2 y(x)}=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 844

\(5 y'(x)^2+3 x y'(x)-y(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 845

\(5 y'(x)^2+6 x y'(x)-2 y(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 846

\(3 x y(x)^4 y'(x)+9 y'(x)^2+y(x)^5=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 847

\(x y'(x)^2=a\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 848

\(x y'(x)^2=a-x^2\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 849

\(x y'(x)^2=y(x)\)

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

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 850

\(x y'(x)^2-2 y(x)+x=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 851

\(x y'(x)^2+y'(x)=y(x)\)

[_rational, _dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 852

\(x y'(x)^2+2 y'(x)-y(x)=0\)

[_rational, _dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 853

\(x y'(x)^2-2 y'(x)-y(x)=0\)

[_rational, _dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 854

\(x y'(x)^2+4 y'(x)-2 y(x)=0\)

[_rational, _dAlembert]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 855

\(x y'(x)^2+x y'(x)-y(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 856

\(-\left (x^2+1\right ) y'(x)+x y'(x)^2+x=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 857

\(a+x y'(x)^2+y(x) y'(x)=0\)

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

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 858

\(a+x y'(x)^2-y(x) y'(x)=0\)

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

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 859

\(a x+x y'(x)^2-y(x) y'(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 860

\(-x^2+x y'(x)^2+y(x) y'(x)=0\)

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

Solution method Homogeneous ODE, The Isobaric equation

Maple
Mathematica

ODE 861

\(x^3+x y'(x)^2+y(x) y'(x)=0\)

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

Solution method Homogeneous ODE, The Isobaric equation

Maple
Mathematica

ODE 862

\(a y(x)+x y'(x)^2-y(x) y'(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 863

\(y(x) y'(x)+x y'(x)^2-y(x)^4=0\)

[[_homogeneous, `class G`]]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 864

\((a-y(x)) y'(x)+b+x y'(x)^2=0\)

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 865

\(x y'(x)^2+(x-y(x)) y'(x)-y(x)+1=0\)

[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 866

\((a-y(x)+x) y'(x)+x y'(x)^2-y(x)=0\)

[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 867

\(x y'(x)^2-(3 x-y(x)) y'(x)+y(x)=0\)

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

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 868

\(a-b y(x)+b x+x y'(x)^2-y(x)=0\)

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

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 869

\(a+x y'(x)^2-2 y(x) y'(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 870

\(x y'(x)^2+2 y(x) y'(x)-x=0\)

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

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\)

Maple
Mathematica

ODE 871

\(a x+x y'(x)^2-2 y(x) y'(x)=0\)

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

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(y\)

Maple
Mathematica

ODE 872

\(x y'(x)^2-2 y(x) y'(x)+2 y(x)+x=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 873

\(9 x^2+x y'(x)^2-3 y(x) y'(x)=0\)

[[_homogeneous, `class G`]]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 874

\(x y'(x)^2-(3 y(x)+2 x) y'(x)+6 y(x)=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 875

\(-a y(x) y'(x)+b+x y'(x)^2=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 876

\(a y(x) y'(x)+b x+x y'(x)^2=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 877

\(x y'(x)^2-(x y(x)+1) y'(x)+y(x)=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 878

\((1-x) y(x) y'(x)+x y'(x)^2-y(x)^2=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 879

\(\left (1-x^2 y(x)\right ) y'(x)+x y'(x)^2-x y(x)=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 880

\((x+1) y'(x)^2=y(x)\)

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

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 881

\((x+1) y'(x)^2-(y(x)+x) y'(x)+y(x)=0\)

[[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 882

\((a-x) y'(x)^2-b+y(x) y'(x)=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 883

\((a+x) y'(x)^2+y'(x) (\text {a1}+\text {b1} x+\text {c1} y(x))+\text {a2}+\text {b2} x+\text {c2} y(x)=0\)

[_dAlembert]

Solution method Change of variable

Maple
Mathematica

ODE 884

\(2 x y'(x)^2+(2 x-y(x)) y'(x)-y(x)+1=0\)

[_rational, _dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 885

\(3 x y'(x)^2-6 y(x) y'(x)+2 y(x)+x=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 886

\((3 x+1) y'(x)^2-3 (y(x)+2) y'(x)+9=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 887

\((3 x+5) y'(x)^2-(3 y(x)+3) y'(x)+y(x)=0\)

[_rational, _dAlembert]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 888

\(4 x y'(x)^2=(a-3 x)^2\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 889

\(4 x y'(x)^2+2 x y'(x)-y(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 890

\(4 x y'(x)^2-3 y(x) y'(x)+3=0\)

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

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 891

\(4 x y'(x)^2+4 y(x) y'(x)=1\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 892

\(4 y(x) y'(x)+4 x y'(x)^2-y(x)^4=0\)

[[_homogeneous, `class G`]]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 893

\(4 (2-x) y'(x)^2+1=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 894

\(8 y(x) y'(x)+16 x y'(x)^2+y(x)^6=0\)

[[_homogeneous, `class G`]]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 895

\(x^2 y'(x)^2=a^2\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 896

\(x^2 y'(x)^2=y(x)^2\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 897

\(x^2 y'(x)^2+x^2-y(x)^2=0\)

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

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 898

\(x^2 y'(x)^2=(x-y(x))^2\)

[_linear]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 899

\(x^2 y'(x)^2-y(x)^4+y(x)^2=0\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 900

\(x^2 y'(x)^2-x y'(x)+(1-y(x)) y(x)=0\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 901

\(a^2+2 a x y'(x)-2 a y(x)+x^2 y'(x)^2+x^2=0\)

[_rational]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 902

\(x^2 y'(x)^2-2 x y(x) y'(x)+y(x) (y(x)+1)-x=0\)

[[_1st_order, _with_linear_symmetries], _rational]

Solution method Change of variable

Maple
Mathematica

ODE 903

\(-x^4+x^2 y'(x)^2+\left (1-x^2\right ) y(x)^2-2 x y(x) y'(x)=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 904

\(x^2 y'(x)^2-(2 x y(x)+1) y'(x)+y(x)^2+1=0\)

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 905

\(-(a+2 x y(x)) y'(x)+x^2 y'(x)^2+y(x)^2=0\)

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

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 906

\(x^2 y'(x)^2-x (x-2 y(x)) y'(x)+y(x)^2=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 907

\(-4 a+x^2 y'(x)^2+2 x (y(x)+2 x) y'(x)+y(x)^2=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 908

\(x \left (x^3-2 y(x)\right ) y'(x)-\left (2 x^3-y(x)\right ) y(x)+x^2 y'(x)^2=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 909

\(x^2 y'(x)^2+3 x y(x) y'(x)+2 y(x)^2=0\)

[_separable]

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\)

Maple
Mathematica

ODE 910

\(x^3+x^2 y'(x)^2-3 x y(x) y'(x)+2 y(x)^2=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 911

\(x^2 y'(x)^2+4 x y(x) y'(x)-5 y(x)^2=0\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 912

\(x^2 y'(x)^2-4 x (y(x)+2) y'(x)+4 y(x) (y(x)+2)=0\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 913

\(x^2 y'(x)^2-5 x y(x) y'(x)+6 y(x)^2=0\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 914

\(x^2 y'(x)^2+x \left (x^2+x y(x)-2 y(x)\right ) y'(x)+(1-x) \left (x^2-y(x)\right ) y(x)=0\)

[_rational]

Solution method Change of variable

Maple
Mathematica

ODE 915

\(x^2 y'(x)^2+(y(x)+2 x) y(x) y'(x)+y(x)^2=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 916

\(x^2 y'(x)^2+(2 x-y(x)) y(x) y'(x)+y(x)^2=0\)

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

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 917

\(y'(x) \left (a+b x^2 y(x)^3\right )+a b y(x)^3+x^2 y'(x)^2=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 918

\(\left (1-x^2\right ) y'(x)^2=1-y(x)^2\)

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

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 919

\(\left (1-x^2\right ) y'(x)^2+4 x^2+2 x y(x) y'(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 920

\(\left (a^2+x^2\right ) y'(x)^2=b^2\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 921

\(\left (a^2-x^2\right ) y'(x)^2+b^2=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 922

\(\left (a^2-x^2\right ) y'(x)^2=b^2\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 923

\(\left (a^2-x^2\right ) y'(x)^2=x^2\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 924

\(\left (a^2-x^2\right ) y'(x)^2+x^2+2 x y(x) y'(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 925

\(\left (a^2-x^2\right ) y'(x)^2-2 x y(x) y'(x)-y(x)^2=0\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 926

\(\left (a^2+x^2\right ) y'(x)^2+b-2 x y(x) y'(x)+y(x)^2=0\)

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 927

\(\left (2 x^2+1\right ) y'(x)^2+\left (x^2+2 x y(x)+y(x)^2+2\right ) y'(x)+2 y(x)^2+1=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 928

\(4 x^2 y'(x)^2-4 x y(x) y'(x)=8 x^3-y(x)^2\)

[_linear]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 929

\(a x^2 y'(x)^2+(1-a) a x^2-2 a x y(x) y'(x)+y(x)^2=0\)

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

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\)

Maple
Mathematica

ODE 930

\(\left (1-a^2\right ) x^2 y'(x)^2-a^2 x^2-2 x y(x) y'(x)+y(x)^2=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 931

\(x^3 y'(x)^2=a\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 932

\(x^3 y'(x)^2+x y'(x)-y(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 933

\(a+x^3 y'(x)^2+x^2 y(x) y'(x)=0\)

[[_homogeneous, `class G`]]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 934

\(x^3 y'(x)^2-\left (2 x^2 y(x)+1\right ) y'(x)+x y(x)^2=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 935

\(x \left (1-x^2\right ) y'(x)^2-2 \left (1-x^2\right ) y(x) y'(x)+x \left (1-y(x)^2\right )=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 936

\(4 x (a-x) (b-x) y'(x)^2=\left (-2 x (a+b)+a b+2 x^2\right )^2\)

[_quadrature]

Solution method Change of variable

Maple
Mathematica

ODE 937

\(x^4 y'(x)^2-x y'(x)-y(x)=0\)

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

Solution method Homogeneous ODE, The Isobaric equation

Maple
Mathematica

ODE 938

\(x^4 y'(x)^2+2 x^3 y(x) y'(x)-4=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 939

\(x^4 y'(x)^2+x y(x)^2 y'(x)-y(x)^3=0\)

[[_homogeneous, `class G`]]

Solution method Change of variable

Maple
Mathematica

ODE 940

\(x^2 \left (a^2-x^2\right ) y'(x)^2+1=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 941

\(3 x^4 y'(x)^2-x y(x)-y(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 942

\(4 x^5 y'(x)^2+12 x^4 y(x) y'(x)+9=0\)

[[_homogeneous, `class G`]]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 943

\(x^6 y'(x)^2-2 x y'(x)-4 y(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 944

\(x^8 y'(x)^2+3 x y'(x)+9 y(x)=0\)

[[_homogeneous, `class G`]]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 945

\(y(x) y'(x)^2=a\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 946

\(y(x) y'(x)^2=a^2 x\)

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

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 947

\(y(x) y'(x)^2=e^{2 x}\)

[[_1st_order, _with_linear_symmetries]]

Solution method Change of variable

Maple
Mathematica

ODE 948

\(2 a x y'(x)-a y(x)+y(x) y'(x)^2=0\)

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

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\)

Maple
Mathematica

ODE 949

\(-4 a^2 x y'(x)+a^2 y(x)+y(x) y'(x)^2=0\)

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

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 950

\(a x y'(x)+b y(x)+y(x) y'(x)^2=0\)

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

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 951

\(-(a-2 b x) y'(x)-b y(x)+y(x) y'(x)^2=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 952

\(x^3 y'(x)-x^2 y(x)+y(x) y'(x)^2=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method Change of variable

Maple
Mathematica

ODE 953

\(y(x) y'(x)^2+(x-y(x)) y'(x)-x=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 954

\(y(x) y'(x)^2-(y(x)+x) y'(x)+y(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 955

\(y(x) y'(x)^2-(x y(x)+1) y'(x)+x=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 956

\(y(x) y'(x)^2+\left (x-y(x)^2\right ) y'(x)-x y(x)=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 957

\(y(x) y'(x)^2+y(x)=a\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Use new variable

Maple
Mathematica

ODE 958

\((y(x)+x) y'(x)^2+2 x y'(x)-y(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 959

\((2 x-y(x)) y'(x)^2-2 (1-x) y'(x)-y(x)+2=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 960

\(2 y(x) y'(x)^2+(5-4 x) y'(x)+2 y(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 961

\(4 x^3 y'(x)-4 x^2 y(x)+9 y(x) y'(x)^2=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method Change of variable

Maple
Mathematica

ODE 962

\((1-a y(x)) y'(x)^2=a y(x)\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Use new variable

Maple
Mathematica

ODE 963

\(y'(x)^2 (\text {a0}+\text {b0} x+\text {c0} y(x))+y'(x) (\text {a1}+\text {b1} x+\text {c1} y(x))+\text {a2}+\text {b2} x+\text {c2} y(x)=0\)

[_dAlembert]

Solution method Change of variable

Maple
Mathematica

ODE 964

\(\left (x^2-a y(x)\right ) y'(x)^2-2 x y(x) y'(x)=0\)

[_quadrature]

Solution method Change of variable

Maple
Mathematica

ODE 965

\(x y(x) y'(x)^2+(y(x)+x) y'(x)+1=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 966

\(\left (x^2+y(x)^2\right ) y'(x)+x y(x) y'(x)^2+x y(x)=0\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 967

\(\left (x^2-y(x)^2\right ) y'(x)+x y(x) y'(x)^2-x y(x)=0\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 968

\(-\left (x^2-y(x)^2\right ) y'(x)+x y(x) y'(x)^2-x y(x)=0\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 969

\(\left (a+x^2-y(x)^2\right ) y'(x)+x y(x) y'(x)^2-x y(x)=0\)

[_rational]

Solution method Change of variable

Maple
Mathematica

ODE 970

\(-y'(x) \left (a-b x^2+y(x)^2\right )-b x y(x)+x y(x) y'(x)^2=0\)

[_rational]

Solution method The method of Lagrange

Maple
Mathematica

ODE 971

\(\left (3 x^2-2 y(x)^2\right ) y'(x)+x y(x) y'(x)^2-6 x y(x)=0\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 972

\(-2 x y(x) y'(x)+x (x-2 y(x)) y'(x)^2+y(x)^2-2 x y(x)=0\)

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

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\)

Maple
Mathematica

ODE 973

\(6 x y(x) y'(x)+x (x-2 y(x)) y'(x)^2+y(x)^2-2 x y(x)=0\)

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

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\)

Maple
Mathematica

ODE 974

\(y(x)^2 y'(x)^2=a^2\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 975

\(-a^2+y(x)^2 y'(x)^2+y(x)^2=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 976

\(y(x)^2 y'(x)^2-3 x y'(x)+y(x)=0\)

[[_1st_order, _with_linear_symmetries], _rational]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 977

\(-6 x^3 y'(x)+4 x^2 y(x)+y(x)^2 y'(x)^2=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method Change of variable

Maple
Mathematica

ODE 978

\(4 a^2-4 a y(x) y'(x)-4 a x+y(x)^2 y'(x)^2+y(x)^2=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 979

\(y(x)^2 y'(x)^2-(x+1) y(x) y'(x)+x=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 980

\(x^2+2 x y(x) y'(x)+y(x)^2 y'(x)^2=0\)

[_separable]

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\)

Maple
Mathematica

ODE 981

\(a+y(x)^2 y'(x)^2+2 x y(x) y'(x)-y(x)^2=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 982

\(-x^2-2 x y(x) y'(x)+y(x)^2 y'(x)^2+2 y(x)^2=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 983

\(a-x^2-2 x y(x) y'(x)+y(x)^2 y'(x)^2+2 y(x)^2=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 984

\((a-1) b+a x^2+2 a x y(x) y'(x)+(1-a) y(x)^2+y(x)^2 y'(x)^2=0\)

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

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(x\)

Maple
Mathematica

ODE 985

\(\left (1-y(x)^2\right ) y'(x)^2=1\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 986

\(\left (a^2-y(x)^2\right ) y'(x)^2=y(x)^2\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 987

\(\left (a^2-2 a x y(x)+y(x)^2\right ) y'(x)^2+2 a y(x) y'(x)+y(x)^2=0\)

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

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 988

\(\left (a^2 x^2-y(x)^2\right ) y'(x)^2+\left (a^2-1\right ) x^2-2 x y(x) y'(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 989

\(\left ((1-a) x^2+y(x)^2\right ) y'(x)^2+2 a x y(x) y'(x)+(1-a) y(x)^2+x^2=0\)

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

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\)

Maple
Mathematica

ODE 990

\(\left (\left (1-4 a^2\right ) x^2+y(x)^2\right ) y'(x)^2-8 a^2 x y(x) y'(x)+\left (1-4 a^2\right ) y(x)^2+x^2=0\)

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

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\)

Maple
Mathematica

ODE 991

\(\left (\left (1-a^2\right ) x^2+y(x)^2\right ) y'(x)^2+2 a^2 x y(x) y'(x)+\left (1-a^2\right ) y(x)^2+x^2=0\)

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

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\)

Maple
Mathematica

ODE 992

\((y(x)+x)^2 y'(x)^2=y(x)^2\)

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

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 993

\(-\left (x^2-x y(x)-2 y(x)^2\right ) y'(x)+(y(x)+x)^2 y'(x)^2-(x-y(x)) y(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 994

\(2 a^2 y'(x)+\left (a^2-(x-y(x))^2\right ) y'(x)^2+a^2-(x-y(x))^2=0\)

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

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 995

\(x^2+2 x y(x) y'(x)+2 y(x)^2 y'(x)^2+y(x)^2-1=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 996

\(-x^2-2 x y(x) y'(x)+3 y(x)^2 y'(x)^2+4 y(x)^2=0\)

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

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(x\)

Maple
Mathematica

ODE 997

\(3 x^3+2 (3 x+1) x y(x) y'(x)+4 y(x)^2 y'(x)^2=0\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 998

\(\left (x^2-4 y(x)^2\right ) y'(x)^2-4 x^2+6 x y(x) y'(x)+y(x)^2=0\)

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

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 999

\(9 y(x)^2 y'(x)^2-3 x y'(x)+y(x)=0\)

[[_1st_order, _with_linear_symmetries], _rational]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1000

\((2-3 y(x))^2 y'(x)^2=4 (1-y(x))\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 1001

\(a^2 \left (-x^2\right )-3 a^2 x y(x) y'(x)+\left (1-a^2\right ) y(x)^2 y'(x)^2+y(x)^2=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 1002

\((a-b) y(x)^2 y'(x)^2-a b+a y(x)^2-b x^2-2 b x y(x) y'(x)=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 1003

\(a^2 y'(x)^2 \left (b^2-(c x-a y(x))^2\right )+c^2 \left (b^2-(c x-a y(x))^2\right )+2 a b^2 c y'(x)=0\)

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

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 1004

\(a^2 x+y(x)^3 \left (-y'(x)\right )+x y(x)^2 y'(x)^2=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 1005

\(\left (a-x^3-y(x)^3\right ) y'(x)+x^2 y(x)+x y(x)^2 y'(x)^2=0\)

[_rational]

Solution method Change of variable

Maple
Mathematica

ODE 1006

\(-x \left (x^2-2 y(x)^2\right )-2 y(x)^3 y'(x)+x y(x)^2 y'(x)^2=0\)

[_separable]

Solution method Change of variable

Maple
Mathematica

ODE 1007

\(-a+y(x)^3 \left (-y'(x)\right )+2 x y(x)^2 y'(x)^2=0\)

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

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1008

\(4 x^2 y(x)^2 y'(x)^2=\left (x^2+y(x)^2\right )^2\)

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

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 1009

\(-2 x \left (x^3+2 y(x)^2\right ) y(x) y'(x)+\left (2 x^3+y(x)^2\right ) y(x)^2+4 x^2 y(x)^2 y'(x)^2=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 1010

\(4 y(x)^3 y'(x)^2-4 x y'(x)+y(x)=0\)

[[_1st_order, _with_linear_symmetries], _rational]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1011

\(x y(x) \left (x^2+y(x)^2\right ) y'(x)^2-x y(x) \left (x^2+y(x)^2\right )-\left (x^4+x^2 y(x)^2+y(x)^4\right ) y'(x)=0\)

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

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\)

Maple
Mathematica

ODE 1012

\(x \left (a^2 x+y(x) \left (x^2-y(x)^2\right )\right ) y'(x)^2+\left (2 a^2 x y(x)+\left (x^2-y(x)^2\right )^2\right ) y'(x)+a^2 y(x)^2-x \left (x^2-y(x)^2\right ) y(x)=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 1013

\(x \left (a^2 x+y(x) \left (x^2-y(x)^2\right )\right ) y'(x)^2-\left (2 a^2 x y(x)-\left (x^2-y(x)^2\right )^2\right ) y'(x)+a^2 y(x)^2-x \left (x^2-y(x)^2\right ) y(x)=0\)

[_separable]

Solution method Change of variable

Maple
Mathematica

ODE 1014

\(\left (x^2-y(x)^2 \left (x^2+y(x)^2\right )\right ) y'(x)^2-2 x y(x) y'(x)+y(x)^2=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 1015

\(-2 x \left (x^2+2 y(x)^2\right ) y(x) y'(x)+\left (x^4+y(x)^2 \left (x^2-y(x)^2\right )\right ) y'(x)^2+y(x)^4=0\)

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

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\)

Maple
Mathematica

ODE 1016

\(y(x)^5 \left (-y'(x)\right )+3 x y(x)^4 y'(x)^2+1=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 1017

\(-a-3 y(x)^5 y'(x)+9 x y(x)^4 y'(x)^2=0\)

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

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1018

\(9 \left (1-x^2\right ) y(x)^4 y'(x)^2+4 x^2+6 x y(x)^5 y'(x)=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 1019

\(y'(x)^2 \left (a^2 r(x,y(x))-x^2\right )+a^2 r(x,y(x))+2 x y(x) y'(x)-y(x)^2=0\)

[NONE]

Solution method Change of variable, polar coordinates

Maple
Mathematica

ODE 1020

\(y'(x)^2 \left (a r(x,y(x))-x^2\right )+a r(x,y(x))+2 x y(x) y'(x)-y(x)^2=0\)

[NONE]

Solution method Change of variable, polar coordinates

Maple
Mathematica

ODE 1021

\(y'(x)^3=a+b x\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 1022

\(y'(x)^3=a x^n\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 1023

\(y'(x)^3-y(x)+x=0\)

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

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1024

\(y'(x)^3=f(x) \left (a+b y(x)+c y(x)^2\right )\)

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

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 1025

\(y'(x)^3=(y(x)-a)^2 (y(x)-b)^2\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 1026

\(f(x) (y(x)-a)^2 (y(x)-b)^2+y'(x)^3=0\)

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

Solution method Binomial equation \((y')^m + F(x) G(y)=0\)

Maple
Mathematica

ODE 1027

\(f(x) (y(x)-a)^2 (y(x)-b)^2 (y(x)-c)^2+y'(x)^3=0\)

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

Solution method Binomial equation \((y')^m + F(x) G(y)=0\)

Maple
Mathematica

ODE 1028

\(a-b x+y'(x)^3+y'(x)=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(x\)

Maple
Mathematica

ODE 1029

\(y'(x)^3+y'(x)-y(x)=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 1030

\(y'(x)^3+y'(x)=e^{y(x)}\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 1031

\(y'(x)^3-7 y'(x)+6=0\)

[_quadrature]

Solution method Missing Variables ODE, Both independent and dependent variable missing

Maple
Mathematica

ODE 1032

\(a y(x)+y'(x)^3-x y'(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1033

\(y'(x)^3+2 x y'(x)-y(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1034

\(y'(x)^3-2 x y'(x)-y(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1035

\(-a x y'(x)+x^3+y'(x)^3=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Use new variable

Maple
Mathematica

ODE 1036

\(a x y'(x)-a y(x)+y'(x)^3=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 1037

\(-(a+b x) y'(x)+b y(x)+y'(x)^3=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 1038

\(y'(x)^3-y(x) y'(x)-x=0\)

[_dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 1039

\(y'(x)^3-(y(x)+3) y'(x)+x=0\)

[_dAlembert]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1040

\(y'(x)^3-2 y(x) y'(x)+y(x)^2=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 1041

\(-a x y(x) y'(x)+2 a y(x)^2+y'(x)^3=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1042

\(-\left (x^3+x y(x)+y(x)^2\right ) y'(x)+y'(x)^3+x y(x) (y(x)+x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 1043

\(-x y(x)^4 y'(x)+y'(x)^3-y(x)^5=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1044

\(y'(x)^3+e^{3 x-2 y(x)} \left (y'(x)-1\right )=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 1045

\(y'(x)^3+\left (e^{2 x}+e^{3 x}\right ) e^{-2 y(x)} y'(x)-e^{3 x-2 y(x)}=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 1046

\(y'(x)^3+y'(x)^2-y(x)=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 1047

\(y'(x)^3-y'(x)^2+y(x)^2=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Use new variable

Maple
Mathematica

ODE 1048

\(y'(x)^3-y'(x)^2+x y'(x)-y(x)=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 1049

\(a b x-a y'(x)^2+b y(x)+y'(x)^3=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1050

\(\text {a0} y'(x)^2+\text {a1} y'(x)+\text {a2}+\text {a3} y(x)+y'(x)^3=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 1051

\(y'(x)^3+x y'(x)^2-y(x)=0\)

[_dAlembert]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1052

\(-x^3-(1-3 x) x y'(x)+y'(x)^3+(1-3 x) y'(x)^2-1=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Use new variable

Maple
Mathematica

ODE 1053

\(y'(x)^3-y(x) y'(x)^2+y(x)^2=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 1054

\(y'(x)^3+y'(x)^2 (\cos (x) \cot (x)-y(x))-y'(x) (y(x) \cos (x) \cot (x)+1)+y(x)=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 1055

\(y'(x)^3+\left (2 x-y(x)^2\right ) y'(x)^2-2 x y(x)^2 y'(x)=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 1056

\(\left (x^2+2 x y(x)^2-y(x)^2\right ) y'(x)-y(x)^2 \left (x^2-y(x)^2\right )+y'(x)^3-\left (y(x)^2+2 x\right ) y'(x)^2=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 1057

\(-x^3 y(x)^3+x \left (x^2+x y(x)+y(x)^2\right ) y(x) y'(x)-\left (x^2+x y(x)+y(x)^2\right ) y'(x)^2+y'(x)^3=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 1058

\(-x^3 y(x)^6+x \left (x^2+y(x)^4+x y(x)^2\right ) y(x)^2 y'(x)-\left (x^2+y(x)^4+x y(x)^2\right ) y'(x)^2+y'(x)^3=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 1059

\(2 y'(x)^3+x y'(x)-2 y(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 1060

\(2 y'(x)^3+y'(x)^2-y(x)=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 1061

\(x^4 \left (-y'(x)\right )+2 x^3 y(x)+3 y'(x)^3=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1062

\(4 y'(x)^3+4 y'(x)=x\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(x\)

Maple
Mathematica

ODE 1063

\(8 y'(x)^3+12 y'(x)^2=27 (y(x)+x)\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1064

\(a+x y'(x)^3-y(x) y'(x)^2=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 1065

\(x y'(x)^3+(2 x-y(x)) y'(x)^2+(2-2 y(x)) y'(x)-y(x)+1=0\)

[_dAlembert]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 1066

\(-\left (x^2+y(x)+x\right ) y'(x)^2+\left (x^2+x y(x)+y(x)\right ) y'(x)+x y'(x)^3-x y(x)=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 1067

\(4 x^2+x y'(x)^3-2 y(x) y'(x)^2=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1068

\(2 x y'(x)^3-3 y(x) y'(x)^2-x=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 1069

\(4 x y'(x)^3-6 y(x) y'(x)^2+3 y(x)-x=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1070

\(8 x y'(x)^3-12 y(x) y'(x)^2+9 y(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1071

\(x^2 y'(x)^3-2 x y(x) y'(x)^2+y(x)^2 y'(x)+1=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 1072

\(b x \left (a^2-x^2\right ) y'(x)^2+\left (a^2-x^2\right ) y'(x)^3-b x-y'(x)=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 1073

\(x \left (x^5+3 y(x)^2\right ) y'(x)-2 x^5 y(x)-3 x^2 y(x) y'(x)^2+x y'(x)^3-y(x)^3=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 1074

\(2 x^3 y'(x)^3+6 x^2 y(x) y'(x)^2-(1-6 x y(x)) y(x) y'(x)+2 y(x)^3=0\)

[[_homogeneous, `class G`]]

Solution method Change of variable

Maple
Mathematica

ODE 1075

\(8 x^3 y'(x)^3+12 x^2 y(x) y'(x)^2-\left (1-6 x y(x)^2\right ) y'(x)+y(x)^3=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 1076

\(x^4 y'(x)^3-x^3 y(x) y'(x)^2-x^2 y(x)^2 y'(x)+x y(x)^3=1\)

[[_1st_order, _with_linear_symmetries]]

Solution method Change of variable

Maple
Mathematica

ODE 1077

\(x^6 y'(x)^3-x y'(x)-y(x)=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1078

\(y(x) y'(x)^3-3 x y'(x)+3 y(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1079

\(2 y(x) y'(x)^3-3 x y'(x)+2 y(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1080

\(2 y(x) y'(x)^3+3 y(x) y'(x)+x=0\)

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

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1081

\(2 y(x) y'(x)^3-y(x) y'(x)^2+2 x y'(x)-x=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 1082

\((2 y(x)+x) y'(x)^3+3 (y(x)+x) y'(x)^2+(y(x)+2 x) y'(x)=0\)

[_quadrature]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 1083

\(y(x)^2 y'(x)^3-x y'(x)+y(x)=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1084

\(y(x)^2 y'(x)^3+2 x y'(x)-y(x)=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method Change of variable

Maple
Mathematica

ODE 1085

\(4 y(x)^2 y'(x)^3-2 x y'(x)+y(x)=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1086

\(16 y(x)^2 y'(x)^3+2 x y'(x)-y(x)=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method Change of variable

Maple
Mathematica

ODE 1087

\(x \left (x^2+1\right ) y'(x)-x^2 y(x)+y(x)^3 \left (-y'(x)^2\right )+x y(x)^2 y'(x)^3=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 1088

\(x^7 y(x)^2 y'(x)^3+\left (1-3 x^6 y(x)^3\right ) y'(x)^2+3 x^5 y(x)^4 y'(x)-x^4 y(x)^5=0\)

[[_homogeneous, `class G`]]

Solution method Change of variable

Maple
Mathematica

ODE 1089

\(y(x)^3 y'(x)^3-x y'(x)+y(x)=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1090

\(x^3+3 x^2 y(x) y'(x)+y(x)^3 y'(x)^3-(1-3 x) y(x)^2 y'(x)^2-y(x)^2=0\)

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

Solution method Change of variable

Maple
Mathematica

ODE 1091

\(y(x)^4 y'(x)^3-6 x y'(x)+2 y(x)=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1092

\(y'(x)^4=(y(x)-a)^3 (y(x)-b)^2\)

[_quadrature]

Solution method Change of variable

Maple
Mathematica

ODE 1093

\(f(x) (y(x)-a)^3 (y(x)-b)^2+y'(x)^4=0\)

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

Solution method Binomial equation \((y')^m + F(x) G(y)=0\)

Maple
Mathematica

ODE 1094

\(f(x) (y(x)-a)^3 (y(x)-b)^3+y'(x)^4=0\)

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

Solution method Binomial equation \((y')^m + F(x) G(y)=0\)

Maple
Mathematica

ODE 1095

\(f(x) (y(x)-a)^3 (y(x)-b)^3 (y(x)-c)^2+y'(x)^4=0\)

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

Solution method Binomial equation \((y')^m + F(x) G(y)=0\)

Maple
Mathematica

ODE 1096

\(y'(x)^4+x y'(x)-3 y(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1097

\(y'(x)^4-3 (1-x) y'(x)^2+3 (1-2 y(x)) y'(x)+3 x=0\)

[_dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 1098

\(-4 x^2 y(x) y'(x)^2+y'(x)^4+16 x y(x)^2 y'(x)-16 y(x)^3=0\)

[[_homogeneous, `class G`]]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1099

\(y'(x)^4+4 y(x) y'(x)^3+6 y(x)^2 y'(x)^2-\left (1-4 y(x)^3\right ) y'(x)-y(x) \left (3-y(x)^3\right )=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Use new variable

Maple
Mathematica

ODE 1100

\(2 y'(x)^4-y(x) y'(x)-2=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 1101

\(12 x^3+x y'(x)^4-2 y(x) y'(x)^3=0\)

[[_1st_order, _with_linear_symmetries]]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1102

\(a y'(x)^3+b y'(x)^2+y'(x)^5=c y(x)\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 1103

\(a y'(x)^4+b y'(x)^3+c x y'(x)^2+y'(x)^5=c y(x)\)

[_dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 1104

\(3 y'(x)^5-y(x) y'(x)+1=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 1105

\(y'(x)^6=(y(x)-a)^4 (y(x)-b)^3\)

[_quadrature]

Solution method Change of variable

Maple
Mathematica

ODE 1106

\(f(x) (y(x)-a)^4 (y(x)-b)^3+y'(x)^6=0\)

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

Solution method Binomial equation \((y')^m + F(x) G(y)=0\)

Maple
Mathematica

ODE 1107

\(f(x) (y(x)-a)^5 (y(x)-b)^3+y'(x)^6=0\)

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

Solution method Binomial equation \((y')^m + F(x) G(y)=0\)

Maple
Mathematica

ODE 1108

\(f(x) (y(x)-a)^5 (y(x)-b)^4+y'(x)^6=0\)

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

Solution method Binomial equation \((y')^m + F(x) G(y)=0\)

Maple
Mathematica

ODE 1109

\(f(x) (y(x)-a)^5 (y(x)-b)^4 (y(x)-c)^3+y'(x)^6=0\)

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

Solution method Binomial equation \((y')^m + F(x) G(y)=0\)

Maple
Mathematica

ODE 1110

\(x^2 \left (y'(x)^6+3 y(x)^4+3 y(x)^2+1\right )=a^2\)

[_rational]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(x\)

Maple
Mathematica

ODE 1111

\(y'(x)^n=a x^r+b y'(x)^s\)

[_quadrature]

Solution method Change of variable

Maple
Mathematica

ODE 1112

\(y'(x)^n=f(x)^n (y(x)-a)^{n+1} (y(x)-b)^{n-1}\)

[_separable]

Solution method Change of variable

Maple
Mathematica

ODE 1113

\(y'(x)^n=f(x) (y(x)-a)^{n+1}\)

[_separable]

Solution method Binomial equation \((y')^m + F(x) G(y)=0\)

Maple
Mathematica

ODE 1114

\(y'(x)^n=f(x) (y(x)-a)^{n-1} (y(x)-b)^{n-1}\)

[_separable]

Solution method Binomial equation \((y')^m + F(x) G(y)=0\)

Maple
Mathematica

ODE 1115

\(f(x) g(x)+y'(x)^n=0\)

[_quadrature]

Solution method Form \((y')^m + X(x,y)=0\)

Maple
Mathematica

ODE 1116

\(f(x,y(x))+y'(x)^n=0\)

[NONE]

Solution method Form \((y')^m + X(x,y)=0\)

Maple
Mathematica

ODE 1117

\(a y'(x)+y'(x)^n=b y(x)\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 1118

\(y'(x)^n+x y'(x)-y(x)=0\)

[_Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 1119

\(a y'(x)^m+y'(x)^n=b y(x)\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 1120

\(\text {Y1}(y(x)) y'(x)^{n-1}+y'(x)^n=0\)

[_quadrature]

Solution method Form \((y')^m + f_1(x,y) (y')^{m-1} \dots + f_m(x,y)=0\)

Maple
Mathematica

ODE 1121

\(\text {X1}(x,y(x)) y'(x)^{n-1}+y'(x)^n=0\)

[_quadrature]

Solution method Form \((y')^m + f_1(x,y) (y')^{m-1} \dots + f_m(x,y)=0\)

Maple
Mathematica

ODE 1122

\(x^{n-1} y'(x)^n-n x y'(x)+y(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1123

\(\text {X0}(x,y(x)) y'(x)^n+\text {X1}(x,y(x)) y'(x)^{n-1}=0\)

[_quadrature]

Solution method Form \(X_0(x,y) (y')^m + X_1 (x,y) (y')^{m-1} + \dots + X_m(x,y)=0\)

Maple
Mathematica

ODE 1124

\(2 \sqrt {a y'(x)}+x y'(x)-y(x)=0\)

[[_homogeneous, `class G`], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 1125

\((x-y(x)) \sqrt {y'(x)}=a \left (y'(x)+1\right )\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1126

\(3 x y'(x)+2 (y(x)+1)^{3/2}-3 y(x)=0\)

[_separable]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 1127

\(a y'(x)+\sqrt {y'(x)^2+1}=x\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(x\)

Maple
Mathematica

ODE 1128

\(a y'(x)+\sqrt {y'(x)^2+1}=y(x)\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 1129

\(\sqrt {y'(x)^2+1}=x y'(x)\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(y'\)

Maple
Mathematica

ODE 1130

\(-a y(x) y'(x)-a x+\sqrt {y'(x)^2+1}=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1131

\(-x y'(x)^2+\sqrt {y'(x)^2+1}+y(x)=0\)

[_dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 1132

\(\sqrt {a^2+b^2 y'(x)^2}+x y'(x)-y(x)=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 1133

\(\sqrt {a c-b^2} \left (x y'(x)-y(x)\right )+\sqrt {a+2 b y'(x)+c y'(x)^2}=0\)

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 1134

\(a \sqrt {y'(x)^2+1}+x y'(x)-y(x)=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method No Missing Variables ODE, Solve for \(y'\)

Maple
Mathematica

ODE 1135

\(a x \sqrt {y'(x)^2+1}+x y'(x)-y(x)=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1136

\(-a y(x) y'(x)-a x+y(x) \sqrt {y'(x)^2+1}=0\)

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

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1137

\(y(x) \sqrt {y'(x)^2+1}=f\left (y(x) y'(x)+x\right )\)

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

Solution method The method of Lagrange

Maple
Mathematica

ODE 1138

\(\sqrt {\left (a x^2+y(x)^2\right ) \left (y'(x)^2+1\right )}-a x-y(x) y'(x)=0\)

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

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\), Solve for \(p\)

Maple
Mathematica

ODE 1139

\(a \sqrt [3]{y'(x)^3+1}+x y'(x)-y(x)=0\)

[_Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 1140

\(y'(x) \left (a+x \sqrt {y'(x)^2+1}\right )=y(x) \sqrt {y'(x)^2+1}\)

[_Clairaut]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 1141

\(x y'(x)+\cos \left (y'(x)\right )=y(x)\)

[_Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 1142

\(a \cos \left (y'(x)\right )+b y'(x)+x=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(x\)

Maple
Mathematica

ODE 1143

\(y'(x)+\sin \left (y'(x)\right )=x\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(x\)

Maple
Mathematica

ODE 1144

\(y'(x) \sin \left (y'(x)\right )+\cos \left (y'(x)\right )=y(x)\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 1145

\(y'(x)^2 \sin \left (y'(x)\right )=y(x)\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 1146

\(y'(x)^2 \left (\sin \left (y'(x)\right )+x\right )=y(x)\)

[_dAlembert]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1147

\(\left (y'(x)^2+1\right ) \sin ^2\left (y(x)-x y'(x)\right )=1\)

[_Clairaut]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 1148

\(-\sqrt {1-y'(x)^2}+y'(x) \left (\cos ^{-1}\left (y'(x)\right )-x\right )+y(x)=0\)

[_Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 1149

\(\left (y'(x)^2+1\right ) \left (a x+\tan ^{-1}\left (y'(x)\right )\right )+y'(x)=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(x\)

Maple
Mathematica

ODE 1150

\(-y'(x)^2+e^{y'(x)-y(x)}+1=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing, Solve for \(y\)

Maple
Mathematica

ODE 1151

\(y'(x)+\log \left (y'(x)\right )=x\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(x\)

Maple
Mathematica

ODE 1152

\(a+x y'(x)+\log \left (y'(x)\right )=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing, Solve for \(x\)

Maple
Mathematica

ODE 1153

\(a+x y'(x)+\log \left (y'(x)\right )=y(x)\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 1154

\(a+b y(x)+x y'(x)+\log \left (y'(x)\right )=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 1155

\(4 x y'(x)+\log \left (y'(x)\right )-2 y(x)=0\)

[[_1st_order, _with_linear_symmetries], _dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 1156

\(a \left (x y'(x)-y(x)\right )+\log \left (y'(x)\right )=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 1157

\(a \left (\log \left (y'(x)\right )-y'(x)\right )+y(x)-x=0\)

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

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 1158

\(y'(x)+y(x) \log \left (y'(x)\right )-x y(x)-y(x) \log (y(x))=0\)

[_separable]

Solution method No Missing Variables ODE, Solve for \(x\)

Maple
Mathematica

ODE 1159

\(-(x+1) y'(x)+y'(x) \log \left (y'(x)\right )+y(x)=0\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 1160

\(\log \left (x y'(x)-y(x)\right )=y'(x)\)

[[_1st_order, _with_linear_symmetries], _Clairaut]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1161

\(y'(x) \log \left (\sqrt {a+y'(x)^2}+y'(x)\right )-x y'(x)-\sqrt {y'(x)^2+1}+y(x)=0\)

[_Clairaut]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 1162

\(y'(x) \tan \left (y'(x)\right )+\log \left (\cos \left (y'(x)\right )\right )=y(x)\)

[_dAlembert]

Solution method No Missing Variables ODE, Solve for \(y\)

Maple
Mathematica

ODE 1163

\(f\left (y'(x)\right )=0\)

[_quadrature]

Solution method Missing Variables ODE, Both independent and dependent variable missing

Maple
Mathematica

ODE 1164

\(f\left (x,y'(x)\right )=0\)

[_quadrature]

Solution method Missing Variables ODE, Dependent variable missing

Maple
Mathematica

ODE 1165

\(f\left (x y'(x)^2\right )=y(x)-2 x y'(x)\)

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

Solution method Change of variable

Maple
Mathematica

ODE 1166

\(f\left (y(x),y'(x)\right )=0\)

[_quadrature]

Solution method Missing Variables ODE, Independent variable missing

Maple
Mathematica

ODE 1167

\(f\left (y'(x)\right )+x y'(x)=y(x)\)

[_Clairaut]

Solution method Clairaut’s equation and related types, main form

Maple
Mathematica

ODE 1168

\(f\left (y'(x)\right )+x g\left (y'(x)\right )=y(x)\)

[_dAlembert]

Solution method Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Maple
Mathematica

ODE 1169

\(f\left (y'(x),y(x)-x y'(x)\right )=0\)

[_Clairaut]

Solution method Clairaut’s equation and related types, \(f(y-x y', y')=0\)

Maple
Mathematica

ODE 1170

\(f\left (x y'(x),y(x)\right )=0\)

[_separable]

Solution method Homogeneous ODE, The Isobaric equation

Maple
Mathematica

ODE 1171

\(x^n f\left (y'(x),\frac {y(x)}{x}\right )=0\)

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

Solution method Homogeneous ODE, \(x^n f\left ( \frac {y}{x} , y' \right )=0\)

Maple
Mathematica

ODE 1172

\(f\left (y(x) y'(x)+x\right )=y(x)^2 \left (y'(x)^2+1\right )\)

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

Solution method Change of variable

Maple
Mathematica

ODE 1173

\(y(x) f\left (\frac {y'(x)}{y(x)},x\right )=0\)

[_separable]

Solution method Homogeneous ODE, equation of form \(y f(x , \frac {y'}{y})\)

Maple
Mathematica

ODE 1174

\(f\left (x,y(x),y'(x)\right )=0\)

[NONE]

Solution method No Missing Variables ODE

Maple
Mathematica

ODE 1175

\(y''(x)=0\)

[[_2nd_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 1176

\(y''(x)=x+\sin (x)\)

[[_2nd_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 1177

\(y''(x)=\text {c1} \cos (a x)+\text {c2} \sin (b x)\)

[[_2nd_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 1178

\(y''(x)=e^x x\)

[[_2nd_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 1179

\(y''(x)=\text {c1} e^{a x}+\text {c2} e^{-b x}\)

[[_2nd_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 1180

\(y''(x)+y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1181

\(y''(x)-y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1182

\(y''(x)+y(x)=a x\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1183

\(y''(x)+y(x)=a \cos (b x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1184

\(y''(x)+y(x)=8 \cos (x) \cos (2 x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1185

\(y''(x)+y(x)=\sec (x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1186

\(y''(x)+y(x)=a \sin (b x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1187

\(y''(x)+y(x)=\sin (a x) \sin (b x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1188

\(y''(x)+y(x)=4 x \sin (x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1189

\(y''(x)+y(x)=x (\cos (x)-x \sin (x))\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1190

\(y''(x)+y(x)=\tan ^2(x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1191

\(y''(x)+y(x)=e^{-x}\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1192

\(y''(x)+y(x)=e^x \left (x^2-1\right )\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1193

\(y''(x)+y(x)=e^x \sin (2 x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1194

\(y''(x)+y(x)=e^{2 x} \cos (x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1195

\(y''(x)-2 y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1196

\(y''(x)-2 y(x)=4 e^{x^2} x^2\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1197

\(y''(x)+4 y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1198

\(y''(x)+4 y(x)=x \sin ^2(x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1199

\(y''(x)+4 y(x)=2 \tan (x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1200

\(y''(x)+4 y(x)=2 \tan (x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1201

\(y''(x)-a^2 y(x)=x+1\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1202

\(y''(x)=a x+b y(x)\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1203

\(a^2 y(x)+y''(x)=x^2+x+1\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1204

\(a^2 y(x)+y''(x)=\cos (b x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1205

\(a^2 y(x)+y''(x)=\cot (a x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1206

\(a^2 y(x)+y''(x)=\sin (b x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1207

\(y''(x)+x y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1208

\(y(x) (a+b x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1209

\(\left (a+x^2\right ) y(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1210

\(\left (a-x^2\right ) y(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1211

\(y''(x)=\left (a+x^2\right ) y(x)\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1212

\(y(x) \left (a+b^2 x^2\right )+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1213

\(y(x) \left (a+b x+c x^2\right )+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1214

\(y(x) \left (\text {a0}+\text {a1} x^2+x^4\right )+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1215

\(a x^k y(x)+y''(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1216

\(y(x) \left (\text {a0}+\text {a1} x+\text {a2} x^2+\text {a3} x^3+\text {a4} x^4+x^8\right )+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1217

\(y(x) (a+b \cos (2 x))+y''(x)=0\)

[_ellipsoidal]

Solution method TO DO

Maple
Mathematica

ODE 1218

\(y(x) (a+b \cos (2 x)+k \cos (4 x))+y''(x)=0\)

[_ellipsoidal]

Solution method TO DO

Maple
Mathematica

ODE 1219

\(y(x) \left (\sum _{n=0}^m a(n) \cos (2 n x)\right )+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1220

\(y''(x)=2 y(x) \csc ^2(x)\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1221

\(a y(x) \csc ^2(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1222

\(y(x) \left (\text {a0}+\text {a1} \cos ^2(x)+\text {a2} \csc ^2(x)\right )+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1223

\(y''(x)=y(x) \left (a^2+(p-1) p \csc ^2(x)+(q-1) q \sec ^2(x)\right )\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1224

\(y(x) \left (a+b \sin ^2(x)\right )+y''(x)=0\)

[_ellipsoidal]

Solution method TO DO

Maple
Mathematica

ODE 1225

\(y''(x)=y(x) \left (2 \tan ^2(x)+1\right )\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1226

\(y''(x)-y(x) \left (a^2-b e^x\right )=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1227

\(y''(x)-\left (a^2-e^{2 x}\right ) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1228

\(y(x) \left (a+b e^x+c e^{2 x}\right )+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1229

\(a e^{b x} y(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1230

\(y(x) \left (a+b \cosh ^2(x)\right )+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1231

\(y(x) \left (a+b \sinh ^2(x)\right )+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1232

\(y(x) \left (a+b \sin ^2(x)\right )+y''(x)=0\)

[_ellipsoidal]

Solution method TO DO

Maple
Mathematica

ODE 1233

\(\frac {(a+b) y(x)}{x^2}+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1234

\(y''(x)-y'(x)+x y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1235

\(y''(x)+2 y'(x)+y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1236

\(y''(x)-2 y'(x)+y(x)=(x-6) x^2\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1237

\(y''(x)-2 y'(x)+y(x)=e^x\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1238

\(y''(x)-2 y'(x)+y(x)=e^x \left (3 x^2+2 x+1\right )\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1239

\(y''(x)-2 y'(x)+y(x)=e^x \sin (x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1240

\(y''(x)+2 y'(x)+y(x)=x^2+3 e^{2 x}-\cos (x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1241

\(y''(x)-2 y'(x)+y(x)=8 e^{3 x} x^2\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1242

\(y''(x)-2 y'(x)+y(x)=50 \cos (x) \cosh (x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1243

\(y''(x)+2 y'(x)+3 y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1244

\(y''(x)+2 y'(x)+y(x)=e^{-x} \cos (x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1245

\(y''(x)+2 y'(x)+5 y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1246

\(y''(x)+2 y'(x)+5 y(x)=8 \sinh (x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1247

\(-2 \tan (a) y'(x)+\csc ^2(a) y(x)+y''(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1248

\(-2 \tan (a) y'(x)+\csc ^2(a) y(x)+y''(x)=x^2 e^{x \tan (a)}\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1249

\(y''(x)+3 y'(x)+2 y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1250

\(y''(x)+3 y'(x)+2 y(x)=\cos (a x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1251

\(y''(x)+3 y'(x)+2 y(x)=e^x+\sin (x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1252

\(y''(x)-3 y'(x)+2 y(x)=x^2+2 e^{-x}\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1253

\(y''(x)-3 y'(x)+2 y(x)=x e^{a x}\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1254

\(y''(x)-3 y'(x)-4 y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1255

\(y''(x)-3 y'(x)-4 y(x)=10 \cos (2 x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1256

\(y''(x)-4 y'(x)+4 y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1257

\(y''(x)-4 y'(x)+4 y(x)=e^{2 x} \cos ^2(x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1258

\(y''(x)+4 y'(x)+5 y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1259

\(y''(x)+4 y'(x)+5 y(x)=\sin (x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1260

\(y''(x)-4 y'(x)+13 y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1261

\(y''(x)-5 y'(x)+6 y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1262

\(y''(x)-5 y'(x)+6 y(x)=4 e^x x^2\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1263

\(y''(x)-5 y'(x)+6 y(x)=e^{a x}\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1264

\(y''(x)+6 y'(x)+9 y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1265

\(y''(x)+6 y'(x)+9 y(x)=e^{-3 x} \cosh (x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1266

\(y''(x)-7 y'(x)+12 y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1267

\(y''(x)-7 y'(x)+12 y(x)=x\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1268

\(y''(x)+8 y'(x)+16 y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1269

\(y''(x)+8 y'(x)+16 y(x)=4 e^x-e^{2 x}\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1270

\(y''(x)-9 y'(x)+20 y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1271

\(y''(x)-9 y'(x)+20 y(x)=e^{3 x} x^2\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1272

\(2 a y'(x)+b^2 y(x)+y''(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1273

\(2 a y'(x)+b^2 y(x)+y''(x)=c \sin (k x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1274

\(a^2 y(x)-2 a y'(x)+y''(x)=e^x\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1275

\(\left (a^2+b^2\right )^2 y(x)-4 a b y'(x)+y''(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1276

\(a y'(x)+b y(x)+y''(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1277

\(a y'(x)+b y(x)+y''(x)=f(x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1278

\(a y'(x)+y(x) (b+c x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1279

\(a y'(x)+y(x) \left (b+c x^2\right )+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1280

\(a y'(x)+y(x) \left (b+c e^x\right )+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1281

\(b e^{2 a x} y(x)+a y'(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1282

\(a y'(x)+b e^{k x} y(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1283

\(y''(x)+x y'(x)+y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1284

\(y''(x)+x y'(x)-y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1285

\(y''(x)-x y'(x)+2 y(x)=0\)

[_Hermite]

Solution method TO DO

Maple
Mathematica

ODE 1286

\(n y(x)+y''(x)-x y'(x)=0\)

[_Hermite]

Solution method TO DO

Maple
Mathematica

ODE 1287

\(-a y(x)+y''(x)-x y'(x)=0\)

[_Hermite]

Solution method TO DO

Maple
Mathematica

ODE 1288

\(y''(x)-x y'(x)-(1-x) y(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1289

\(y''(x)-2 x y'(x)+6 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1290

\(y''(x)+2 x y'(x)-8 y(x)=0\)

[_erf]

Solution method TO DO

Maple
Mathematica

ODE 1291

\(2 n y(x)+y''(x)-2 x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1292

\(-\left (-x^2-x+1\right ) y(x)+y''(x)-(2 x+1) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1293

\(2 \left (2 x^2+1\right ) y(x)+y''(x)+4 x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1294

\(-\left (3-4 x^2\right ) y(x)+y''(x)-4 x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1295

\(-\left (3-4 x^2\right ) y(x)+y''(x)-4 x y'(x)=e^{x^2}\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1296

\(a^2 x^2 y(x)-2 a x y'(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1297

\(a x y'(x)+b y(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1298

\((a+b x) y'(x)+c y(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1299

\((\text {a0}+\text {b0} x) y'(x)+y(x) (\text {a1}+\text {b1} x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1300

\((\text {a0}+\text {b0} x) y'(x)+y(x) \left (\text {a1}+\text {b1} x+\text {c1} x^2\right )+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1301

\(-2 a \left (1-2 a x^2\right ) y(x)-4 a x y'(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1302

\(x^2 \left (-y'(x)\right )+y''(x)+x y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1303

\(x^2 \left (-y'(x)\right )+y''(x)+x y(x)=x\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1304

\(x^2 y'(x)+y''(x)-4 x y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1305

\(x^4 y'(x)-x^3 y(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1306

\(a (k+1) x^{k-1} y(x)+a x^k y'(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1307

\(a k x^{k-1} y(x)+a x^k y'(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1308

\(-a x^{k-1} y(x)+a x^k y'(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1309

\(a x^k y'(x)+b x^{k-1} y(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1310

\(y''(x)-\cot (x) y'(x)+2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1311

\(k (k+1) y(x)+y''(x)+\cot (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1312

\(y''(x)+\cot (x) y'(x)-y(x) \csc ^2(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1313

\(y(x) \left (p (p+1)-k^2 \csc ^2(x)\right )+y''(x)+\cot (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1314

\(y(x) \left (\text {a0}+4 \text {a1} \sin ^2(x)-\text {a2} \csc ^2(x)\right )+y''(x)+\cot (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1315

\(y''(x)+2 \cot (x) y'(x)+3 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1316

\(y''(x)+2 \cot (x) y'(x)+3 y(x)=e^x \csc (x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1317

\(a \cot (x) y'(x)+y(x) \left (b+k^2 \cos ^2(x)\right )+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1318

\(y(x) \left (a \cot ^2(x)+b \cot (x) \csc (x)+c \csc ^2(x)\right )+k \cot (x) y'(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1319

\(y''(x)-\cot (2 x) y'(x)+2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1320

\(a y(x) \tan ^2(x)+y''(x)-2 \cot (2 x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1321

\(a \cot (b x) y'(x)+c y(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1322

\(\left (b^2-a^2\right ) y(x)+2 a \cot (a x) y'(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1323

\(a y(x) \tan ^2\left (\frac {x}{2}\right )+y''(x)-\csc (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1324

\(y''(x)+y'(x) (\cot (x)+\csc (x))=a \csc (x)+1\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1325

\(y''(x)-\csc (2 x) y'(x)+y(x) \left (\sin ^2(x)+2\right ) \csc ^2(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1326

\(a y(x) \csc ^2(x)+y''(x)+(\cos (x)+2) \csc (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1327

\(y''(x)-(3 \cos (x)+2) \csc (x) y'(x)-2 y(x) (\cos (x)+1) \sec (x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1328

\(y''(x)-y'(x) (\cot (x)-\sin (x))+y(x) \sin ^2(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1329

\(y''(x)-\sin (x) y'(x)+y(x) (-\cos (x))=a-x+x \log (x)\)

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1330

\(-2 \csc (2 x) \left (1-a \sin ^2(x)\right ) y'(x)+b y(x) \tan ^2(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1331

\(a y(x) \cos ^2(x)+y''(x)+\tan (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1332

\(a y(x) \cot ^2(x)+y''(x)+\tan (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1333

\(-a (a+1) y(x) \csc ^2(x)+y''(x)-\tan (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1334

\(y(x) \left (a \cos ^2(x)-\sec ^2(x)\right )+y''(x)-\tan (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1335

\(y''(x)+2 \tan (x) y'(x)-y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1336

\(y''(x)+2 \tan (x) y'(x)-y(x)=(x+1) \sec (x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1337

\(y''(x)+2 \tan (x) y'(x)+3 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1338

\(b y(x)+y''(x)-2 \tan (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1339

\(-\left (a^2+1\right ) y(x)+y''(x)-2 \tan (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1340

\(-\left (a^2+1\right ) y(x)+y''(x)-2 \tan (x) y'(x)=\sin (x)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1341

\(a \tan (x) y'(x)+b y(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1342

\(y''(x)-\left (2 e^x+1\right ) y'(x)+e^{2 x} y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1343

\(y(x) \left (\text {a0}+4 \text {a1} \sinh ^2(x)-\text {a2} \text {csch}^2(x)\right )+y''(x)+\coth (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1344

\(y(x) \left (\text {a0}+4 \text {a1} \cosh ^2(x)-\text {a2} \text {sech}^2(x)\right )+y''(x)+\tanh (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1345

\(b y(x)+y''(x)+2 \tanh (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1346

\(a \tanh (x) y'(x)+b y(x)+y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1347

\(f(x) y'(x)+y''(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1348

\(a k x^{k-1} y(x)+2 a x^k y'(x)+2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1349

\(3 y''(x)-10 y'(x)+3 y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1350

\(4 y''(x)=\left (a+x^2\right ) y(x)\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1351

\(\left (4 a-x^2+2\right ) y(x)+4 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1352

\(4 y''(x)-8 y'(x)+3 y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1353

\(x y''(x)+y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1354

\((a+x) y(x)+x y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1355

\(x y''(x)+y'(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1356

\(x y''(x)+y'(x)=x^n\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1357

\(x y''(x)+y'(x)-y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1358

\(x y''(x)+y'(x)-(x+1) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1359

\(4 x^3 y(x)+x y''(x)-y'(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1360

\(-a^2 x^3 y(x)+x y''(x)-y'(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1361

\(x^3 \left (e^{x^2}-k^2\right ) y(x)+x y''(x)-y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1362

\(x y''(x)+2 y'(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1363

\(x y''(x)+2 y'(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1364

\(x y''(x)+2 y'(x)-x y(x)=e^x\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1365

\(a x y(x)+x y''(x)+2 y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1366

\(a x^2 y(x)+x y''(x)+2 y'(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1367

\(a y'(x)+x y''(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1368

\((a+1) y'(x)+x y''(x)+y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1369

\((1-a) y'(x)+x y''(x)+y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1370

\((a+1) y'(x)+x y''(x)-y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1371

\(2 n y'(x)+x y''(x)-y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1372

\(a y'(x)+b y(x)+x y''(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1373

\(a y'(x)+b x y(x)+x y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1374

\(a y'(x)+y(x) (\text {b1}+\text {b2} x)+x y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1375

\(a y'(x)+y(x) \left (\text {a1}+\text {b1} x+\text {c1} x^2\right )+x y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1376

\(a y'(x)+b x^k y(x)+x y''(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1377

\(x y''(x)-(x+1) y'(x)+y(x)=0\)

[_Laguerre]

Solution method TO DO

Maple
Mathematica

ODE 1378

\(n y(x)+x y''(x)+(1-x) y'(x)=0\)

[_Laguerre]

Solution method TO DO

Maple
Mathematica

ODE 1379

\((k-x+1) y'(x)+n y(x)+x y''(x)=0\)

[_Laguerre]

Solution method TO DO

Maple
Mathematica

ODE 1380

\(x y''(x)-(x+1) y'(x)+2 (1-x) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1381

\(x y''(x)-(2-x) y'(x)-y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1382

\(x y''(x)-(x+3) y'(x)+y(x)=0\)

[_Laguerre]

Solution method TO DO

Maple
Mathematica

ODE 1383

\(x y''(x)-(x+3) y'(x)+3 y(x)=0\)

[_Laguerre]

Solution method TO DO

Maple
Mathematica

ODE 1384

\((a+x) y'(x)+b y(x)+x y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1385

\(-a y(x)+(c-x) y'(x)+x y''(x)=0\)

[_Laguerre]

Solution method TO DO

Maple
Mathematica

ODE 1386

\(x y''(x)+(1-2 x) y'(x)-(1-x) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1387

\(x y''(x)-(2 x+1) y'(x)+(x+1) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1388

\(x y''(x)-(2 x+1) y'(x)+(x+1) y(x)=x^2-x-1\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1389

\((a+b x) y'(x)+c y(x)+x y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1390

\((\text {a1}+\text {b1} x) y'(x)+y(x) (\text {a2}+\text {b2} x)+x y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1391

\(-2 (a+b x) y'(x)+y(x) (2 a+b x)+x y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1392

\(y'(x) (x (a+b)+m+n)+y(x) (a b x+a n+b m)+x y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1393

\(x y''(x)-\left (1-x^2\right ) y'(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1394

\(-\left (4-x^2\right ) y'(x)+x y''(x)+2 x y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1395

\(x^3 y(x)-\left (2 x^2+1\right ) y'(x)+x y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1396

\(-8 x^3 y(x)-\left (2 x^2+1\right ) y'(x)+x y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1397

\(-8 x^3 y(x)-\left (2 x^2+1\right ) y'(x)+x y''(x)=4 e^{-x^2} x^3\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1398

\(\left (4 x^2+1\right ) y'(x)+4 x \left (x^2+1\right ) y(x)+x y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1399

\(-\left (1-2 a x^3\right ) y'(x)+a x^2 \left (a x^3+1\right ) y(x)+x y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1400

\((x f(x)+2) y'(x)+f(x) y(x)+x y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1401

\((1-x) y''(x)+x y'(x)-y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1402

\((1-x) y''(x)+x y'(x)-y(x)=(1-x)^2\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1403

\((3-x) y''(x)-(9-4 x) y'(x)+3 (2-x) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1404

\((a-x) y''(x)-2 y'(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1405

\((a+x) y''(x)+(\text {a1}+\text {b1} x) y'(x)+y(x) (\text {a2}+\text {b2} x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1406

\(2 x y''(x)+y'(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1407

\(a y(x)+2 x y''(x)+y'(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1408

\(-a y(x)+2 x y''(x)+y'(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1409

\(y(x) (a+b x)+2 x y''(x)+y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1410

\(-\left (2 x^2+1\right ) y'(x)+2 x y''(x)-x y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1411

\((1-2 x) y''(x)-(x+2) y'(x)-y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1412

\((1-2 x) y''(x)-(4-3 x) y'(x)+(3-x) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1413

\(4 y''(x)+2 y'(x)+y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1414

\(4 y''(x)-2 y'(x)-y(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1415

\(4 x y''(x)+4 \coth (x) y'(x)+y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1416

\(y(x) (a+b x)+16 x y''(x)+8 y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1417

\((a+b x) y''(x)+c y'(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1418

\((\text {a0}+\text {b0} x) y''(x)+(\text {a1}+\text {b1} x) y'(x)+y(x) (\text {a2}+\text {b2} x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1419

\((1-x \cot (x)) y''(x)-x y'(x)+y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1420

\(x^2 y''(x)=a+b x\)

[[_2nd_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 1421

\(x^2 y''(x)=2 y(x)\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1422

\(x^2 y''(x)=6 y(x)\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1423

\(x^2 y''(x)=12 y(x)\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1424

\(a y(x)+x^2 y''(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1425

\(y(x) (a+b x)+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1426

\(x^2 y''(x)-\left (2-x^2\right ) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1427

\(x^2 y''(x)-\left (2-x^2\right ) y(x)=x^4\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1428

\(x^2 y''(x)-\left (a^2 x^2+2\right ) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1429

\(x^2 y''(x)-\left (6-a^2 x^2\right ) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1430

\(x^2 y''(x)-y(x) \left (a^2 x^2+n (n+1)\right )=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1431

\(x^2 y''(x)-y(x) \left ((n-1) n-a^2 x^2\right )=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1432

\(y(x) \left (a+b x+c x^2\right )+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1433

\(x^2 y''(x)-y(x) \left ((a-1) a-b x^k\right )=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1434

\(x^k y(x) \left (a+b x^k\right )+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1435

\(-b y(x) \left (a+b x^2\right )+a y'(x)+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1436

\(x^2 y''(x)+x y'(x)+y(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1437

\(x^2 y''(x)+x y'(x)-y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1438

\(x^2 y''(x)-x y'(x)+y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1439

\(x^2 y''(x)+x y'(x)-y(x)=a x^2\)

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1440

\(x^2 y''(x)-x y'(x)+y(x)=x^2 (x+3)\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1441

\(x^2 y''(x)-x y'(x)+y(x)=3 x^3\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1442

\(x^2 y''(x)+x y'(x)+y(x)=\log (x)\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1443

\(x^2 y''(x)-x y'(x)+2 y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1444

\(x^2 y''(x)-x y'(x)+2 y(x)=x \log (x)\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1445

\(x^2 y''(x)-x y'(x)-3 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1446

\(a^2 (-y(x))+x^2 y''(x)+x y'(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1447

\(y(x) (a+b x)+x^2 y''(x)+x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1448

\(-\left (p^2-x^2\right ) y(x)+x^2 y''(x)+x y'(x)=0\)

[_Bessel]

Solution method TO DO

Maple
Mathematica

ODE 1449

\(-\left (p^2+x^2\right ) y(x)+x^2 y''(x)+x y'(x)=0\)

[[_Bessel, _modified]]

Solution method TO DO

Maple
Mathematica

ODE 1450

\(-\left (p^2+i x^2\right ) y(x)+x^2 y''(x)+x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1451

\(-y(x) \left (p^2-a^2 x^2\right )+x^2 y''(x)+x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1452

\(-y(x) \left (a+b x+c x^2\right )+x^2 y''(x)+x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1453

\(-y(x) \left (4 a x^2+n^2-x^4\right )+x^2 y''(x)+x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1454

\(-y(x) \left (a^2+b^2 x^2+c^2 x^4\right )+x^2 y''(x)+x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1455

\((m+1) a(m) x^m y(x)+x^2 y''(x)+x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1456

\((a+x) y'(x)+x^2 y''(x)-y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1457

\(x^2 y''(x)-2 x y'(x)+2 y(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1458

\(x^2 y''(x)-2 x y'(x)+2 y(x)=4 x^3\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1459

\(x^2 y''(x)-2 x y'(x)+2 y(x)=x^3 \sin (x)\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1460

\(x^2 y''(x)-2 x y'(x)+2 y(x)=2 x \log (x)\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1461

\(x^2 y''(x)-2 x y'(x)+2 y(x)=x^5 \log (x)\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1462

\(x^2 y''(x)+2 x y'(x)-6 y(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1463

\(x^2 y''(x)+2 x y'(x)-6 y(x)=2-x\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1464

\(\left (a^2 x^2+2\right ) y(x)+x^2 y''(x)-2 x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1465

\(-y(x) \left (n (n+1)-a^2 x^2\right )+x^2 y''(x)+2 x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1466

\(y(x) \left (a+b x^2\right )+x^2 y''(x)+2 x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1467

\(a y(x)+x^2 y''(x)-2 (1-x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1468

\(x^2 y''(x)+3 x y'(x)+y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1469

\(x^2 y''(x)+3 x y'(x)+y(x)=x\)

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1470

\(x^2 y''(x)+3 x y'(x)+y(x)=a-x+x \log (x)\)

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1471

\(x^2 y''(x)-3 x y'(x)+4 y(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1472

\(x^2 y''(x)-3 x y'(x)+4 y(x)=5 x\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1473

\(x^2 y''(x)-3 x y'(x)-5 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1474

\(x^2 y''(x)-3 x y'(x)-5 y(x)=x^2 \log (x)\)

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1475

\(x^2 y''(x)+4 x y'(x)+2 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1476

\(x^2 y''(x)+4 x y'(x)+2 y(x)=e^x\)

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1477

\(x^2 y''(x)+4 x y'(x)+2 y(x)=\log (x+1)\)

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1478

\(x^2 y''(x)-4 x y'(x)+6 y(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1479

\(x^2 y''(x)-4 x y'(x)+6 y(x)=x^2 \left (x^2-1\right )\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1480

\(x^2 y''(x)+\left (2-x^2\right ) y(x)+4 x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1481

\(x^2 y''(x)+\left (x^2+6\right ) y(x)+4 x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1482

\(x^2 y''(x)+5 x y'(x)+13 y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1483

\(x^2 y''(x)-7 x y'(x)+16 y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1484

\(y(x) \left (a (a+1)+b^2 x^2\right )-2 a x y'(x)+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1485

\(\text {a1} x y'(x)+\text {a2} y(x)+x^2 y''(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1486

\(\text {a1} x y'(x)+y(x) (\text {a2}+\text {b2} x)+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1487

\(\text {a1} x y'(x)+y(x) \left (\text {a2}+\text {b2} x^2\right )+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1488

\(\text {a1} x y'(x)+y(x) \left (\text {a2}+\text {b2} x+\text {c2} x^2\right )+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1489

\(a x y'(x)+y(x) \left (b+c x^3\right )+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1490

\(a x y'(x)+x^2 y(x) \left (\text {a1}+\text {b1} x^2\right )+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1491

\(a x y'(x)+y(x) \left (b+c x^{2 k}\right )+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1492

\((a+b x) y'(x)+c y(x)+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1493

\(-2 a x y'(x)+a (a+1) y(x)+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1494

\(-2 a x y'(x)+a (a+1) y(x)+x^2 y''(x)=e^x x^{a+2}\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1495

\(y(x) \left (a (a+1)+b^2 x^2\right )-2 a x y'(x)+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1496

\(y(x) (a+b x)+2 a x y'(x)+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1497

\(x^2 y''(x)-x^2 y'(x)-2 x^2 y(x)=2 x^2 \log (x)+x+1\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1498

\(y(x) \left (a+b x^2\right )+x^2 y''(x)+x^2 y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1499

\(x^2 y''(x)-\left (1-x^2\right ) y'(x)-y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1500

\(x^2 y''(x)+(1-x) x y'(x)-(1-x) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1501

\(x^2 y''(x)-(x+2) x y'(x)+(x+2) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1502

\(x^2 y''(x)-(x+2) x y'(x)+(x+2) y(x)=x^3\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1503

\(x^2 y''(x)+(2-x) x y'(x)-(3 x+2) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1504

\(x^2 y''(x)+(x+3) x y'(x)-y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1505

\(x^2 y''(x)-2 (x+1) x y'(x)+2 (x+1) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1506

\(a x^2 y'(x)+x^2 y''(x)-2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1507

\(-x (a x+5) y'(x)+(3 a x+5) y(x)+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1508

\(x (\text {a1}+\text {b1} x) y'(x)+y(x) \left (\text {a2}+\text {b2} x+\text {c2} x^2\right )+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1509

\(x^3 y'(x)+x^2 y''(x)-\left (2-x^2\right ) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1510

\(x^2 y''(x)+\left (1-x^2\right ) x y'(x)-\left (x^2+1\right ) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1511

\(4 x^3 y'(x)+x^2 y''(x)+\left (4 x^4+2 x^2+1\right ) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1512

\(x y'(x) \left (\text {a0}+\text {b0} x^k\right )+y(x) \left (\text {a1}+\text {b1} x^k+\text {c1} x^{2 k}\right )+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1513

\(x y'(x) \left (\text {a0}+\text {a1} x^r+\text {a2} x^s\right )+y(x) \left (\text {b0}+\text {b1} x^r+\text {b2} x^{2 r}+\text {b3} x^s+\text {b4} x^{2 s}+\text {b5} x^{r+s}\right )+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1514

\(a y(x)+x^2 y''(x)+2 x^2 \cot (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1515

\(-y(x) (a-x \cot (x))+x^2 y''(x)+x (2 x \cot (x)+1) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1516

\(a y(x)+x^2 y''(x)-2 x^2 \tan (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1517

\(-y(x) (a+x \tan (x))+x^2 y''(x)+x (1-2 x \tan (x)) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1518

\(y(x) \left (f(x) \left (\text {a1}+\text {b1} x^k-1\right )+\text {a2}+\text {b2} x^k+\text {c2} x^{2 k}+f'(x)+f(x)^2\right )+x y'(x) \left (\text {a1}+\text {b1} x^k+2 f(x)\right )+x^2 y''(x)=0\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 1519

\(\left (x^2+1\right ) y''(x)-2 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1520

\(a+\left (x^2+1\right ) y''(x)-x y'(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1521

\(\left (1-x^2\right ) y''(x)+x y'(x)=x\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1522

\(\left (x^2+1\right ) y''(x)-x y'(x)+y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1523

\(\left (1-x^2\right ) y''(x)+x y'(x)-y(x)=0\)

[_Gegenbauer]

Solution method TO DO

Maple
Mathematica

ODE 1524

\(\left (1-x^2\right ) y''(x)-x y'(x)+y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1525

\(\left (1-x^2\right ) y''(x)-x y'(x)-y(x)=0\)

[_Gegenbauer, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1526

\(\left (1-x^2\right ) y''(x)+x y'(x)-y(x)=x \left (1-x^2\right )^{3/2}\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1527

\(\left (1-x^2\right ) y''(x)+x y'(x)+3 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1528

\(\left (x^2+1\right ) y''(x)+x y'(x)-4 y(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1529

\(\left (x^2+1\right ) y''(x)+x y'(x)-4 y(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1530

\(n^2 y(x)+\left (1-x^2\right ) y''(x)-x y'(x)=0\)

[_Gegenbauer, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1531

\(a^2 y(x)+\left (x^2+1\right ) y''(x)+x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1532

\(a^2 y(x)+\left (1-x^2\right ) y''(x)-x y'(x)=0\)

[_Gegenbauer, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1533

\(y(x) \left (a+b x^2\right )+\left (1-x^2\right ) y''(x)-x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1534

\(y(x) \left (\sum _{m=0}^n a(m) x^{2 m}\right )+\left (1-x^2\right ) y''(x)-x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1535

\(\left (1-x^2\right ) y''(x)-2 x y'(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1536

\(a+\left (1-x^2\right ) y''(x)-2 x y'(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1537

\(\left (x^2+1\right ) y''(x)+2 x y'(x)-2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1538

\(\left (x^2+1\right ) y''(x)-2 x y'(x)+2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1539

\(\left (1-x^2\right ) y''(x)+2 x y'(x)-2 y(x)=\left (1-x^2\right )^2\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1540

\(n (n+1) y(x)+\left (1-x^2\right ) y''(x)-2 x y'(x)=0\)

[_Gegenbauer]

Solution method TO DO

Maple
Mathematica

ODE 1541

\(n (n+1) y(x)+\left (1-x^2\right ) y''(x)-2 x y'(x)=\frac {2 ((-n-1) x P_n(x)+(n+1) P_{n+1}(x))}{x^2-1}\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1542

\(-p (p+1) y(x)+\left (x^2+1\right ) y''(x)+2 x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1543

\(p (p+1) y(x)+\left (1-x^2\right ) y''(x)-2 x y'(x)=0\)

[_Gegenbauer]

Solution method TO DO

Maple
Mathematica

ODE 1544

\(n (n+2) y(x)+\left (1-x^2\right ) y''(x)-3 x y'(x)=0\)

[_Gegenbauer]

Solution method TO DO

Maple
Mathematica

ODE 1545

\(-a y(x)+\left (1-x^2\right ) y''(x)-3 x y'(x)=0\)

[_Gegenbauer]

Solution method TO DO

Maple
Mathematica

ODE 1546

\(\left (x^2+1\right ) y''(x)+4 x y'(x)+2 y(x)=2 (\cos (x)-x)\)

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1547

\(\left (x^2+1\right ) y''(x)-4 x y'(x)+6 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1548

\(\left (1-x^2\right ) y''(x)-\left (x^2+1\right ) y(x)-4 x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1549

\(\left (1-x^2\right ) y''(x)-6 x y'(x)-4 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1550

\(n y(x) (a+b+n+1)+(-x (a+b+2)-a+b) y'(x)+\left (1-x^2\right ) y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1551

\(p (2 k+p) y(x)-(2 k+1) x y'(x)+\left (1-x^2\right ) y''(x)=0\)

[_Gegenbauer]

Solution method TO DO

Maple
Mathematica

ODE 1552

\(n y(x) (a+b+n+1)+(-x (a+b+2)-a+b) y'(x)+\left (1-x^2\right ) y''(x)=0\)

[_Gegenbauer]

Solution method TO DO

Maple
Mathematica

ODE 1553

\(-(k-p) (k+p+1) y(x)-2 (k+1) x y'(x)+\left (1-x^2\right ) y''(x)=0\)

[_Gegenbauer]

Solution method TO DO

Maple
Mathematica

ODE 1554

\(-2 a x y'(x)+(1-a) a y(x)+\left (1-x^2\right ) y''(x)=0\)

[_Gegenbauer]

Solution method TO DO

Maple
Mathematica

ODE 1555

\(a x y'(x)-(2-a) y(x)+\left (x^2+1\right ) y''(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1556

\(a x y'(x)+b y(x)+\left (1-x^2\right ) y''(x)=0\)

[_Gegenbauer]

Solution method TO DO

Maple
Mathematica

ODE 1557

\(a x y'(x)+y(x) \left (\text {a0}+\text {b0} x+\text {c0} x^2\right )+\left (1-x^2\right ) y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1558

\((a+b x) y'(x)+c y(x)+\left (1-x^2\right ) y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1559

\(\left (a^2-x^2\right ) y''(x)+y(x) \left (b^2+c^2 x^2\right )-x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1560

\(\left (a^2-x^2\right ) y''(x)-8 x y'(x)-12 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1561

\((1-x) x y''(x)+2 y'(x)+y(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1562

\((1-x) x y''(x)-2 y'(x)+2 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1563

\((1-x) x y''(x)+2 y'(x)+6 y(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1564

\((1-x) x y''(x)-2 y'(x)+6 y(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1565

\((1-x) x y''(x)+3 y'(x)+2 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1566

\((1-x) x y''(x)-3 y'(x)+2 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1567

\((1-x) x y''(x)-3 y'(x)+2 y(x)=x \left (3 x^3+1\right )\)

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1568

\(-a y'(x)+(1-x) x y''(x)+2 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1569

\(x (x+1) y''(x)+(1-x) y'(x)+y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1570

\((1-x) x y''(x)-(x+1) y'(x)+y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1571

\((1-x) x y''(x)-(x+4) y'(x)+4 y(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1572

\((1-x) x y''(x)+2 x y'(x)-2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1573

\((1-x) x y''(x)+(1-2 x) y'(x)+6 y(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1574

\(p (p+1) y(x)+(1-x) x y''(x)+(1-2 x) y'(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1575

\((1-x) x y''(x)+(1-x) y'(x)+2 y(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1576

\((1-x) x y''(x)-3 x y'(x)-y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1577

\(x (x+1) y''(x)+(3 x+2) y'(x)+y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1578

\((1-x) x y''(x)+(1-4 x) y'(x)-2 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1579

\((1-x) x y''(x)-2 (2 x+1) y'(x)-2 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1580

\((1-x) x y''(x)-2 (1-2 x) y'(x)-6 y(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1581

\((p-k) (k+p+1) y(x)+(k+1) (1-2 x) y'(x)+(1-x) x y''(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1582

\((c-(a+1) x) y'(x)+n (a+n) y(x)+(1-x) x y''(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1583

\((a+b x) y'(x)+c y(x)+x (x+1) y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1584

\(y'(x) (c-x (a+b+1))-a b y(x)+(1-x) x y''(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1585

\(-(a-(2-a) x) y'(x)-a y(x)+x (x+1) y''(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1586

\(-(a-(2-a) x) y'(x)-a y(x)+x (x+1) y''(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1587

\((a+b x) y'(x)+c y(x)+(1-x) x y''(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1588

\(y(x) \left (\sum _{m=0}^n a(m) x^m\right )+a (1-2 x) y'(x)+x (x+1) y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1589

\(\left (-x^2-x+2\right ) y''(x)+(1-x) x y'(x)+x (6 x+7) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1590

\((2-x) x y''(x)+2 (1-x) y'(x)+2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1591

\(-\left (2-x^2\right ) y'(x)+(2-x) x y''(x)+2 (1-x) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1592

\((1-x)^2 y''(x)-4 (1-x) y'(x)+2 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1593

\((1-x)^2 y''(x)-4 (1-x) y'(x)+2 y(x)=\cos (x)\)

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1594

\((x+1)^2 y''(x)-4 (x+1) y'(x)+6 y(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1595

\((x+1)^2 y''(x)-4 (x+1) y'(x)+6 y(x)=x\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1596

\(-\left (-x^2-x+1\right ) y'(x)+(x+1)^2 y''(x)-(x+2) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1597

\((1-x)^2 y''(x)-2 (1-x)^2 y'(x)+(1-x)^2 y(x)=e^x\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1598

\(\left (x^2+3 x+4\right ) y''(x)+\left (x^2+x+1\right ) y'(x)-(2 x+3) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1599

\((x+2)^2 y''(x)-(x+2) y'(x)+2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1600

\((2-x)^2 y''(x)+(2-x) y'(x)-3 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1601

\(x (\text {a0}+x) y''(x)+(\text {a1}+\text {b1} x) y'(x)+\text {a2} y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1602

\(-4 (a+x) y'(x)+(\text {a0}+x)^2 y''(x)+6 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1603

\(2 x^2 y''(x)-x y'(x)+y(x)=x^2\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1604

\(2 x^2 y''(x)+x y'(x)-3 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1605

\(2 x^2 y''(x)-(2 x+7) x y'(x)+2 (x+5) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1606

\(2 x^2 y''(x)-(1-4 x) x y'(x)-2 (1-3 x) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1607

\(2 x^2 y''(x)-(1-4 x) x y'(x)-2 (1-3 x) y(x)=x^3 (x+1)\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1608

\(\left (2 x^2+1\right ) y''(x)+3 x y'(x)-3 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1609

\(2 a^2 y(x)+2 \left (1-x^2\right ) y''(x)-x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1610

\(2 x (x+1) y''(x)+y'(x)-4 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1611

\(2 (1-x) x y''(x)+(x+1) y'(x)-y(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1612

\(2 (1-x) x y''(x)+(1-x) y'(x)+y(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1613

\(2 (1-x) x y''(x)+(1-2 x) y'(x)-2 y(x)=0\)

[_Jacobi, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1614

\(2 (1-x) x y''(x)+(1-2 x) y'(x)+8 y(x)=0\)

[_Jacobi, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1615

\(a y(x)+2 (1-x) x y''(x)-(1-2 x) y'(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1616

\(y(x) (a+b x)+2 (1-x) x y''(x)+(1-2 x) y'(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1617

\(2 a (a+1) y(x)+2 (1-x) x y''(x)-(3 x+1) y'(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1618

\((1-2 x) (1-x) y''(x)+2 (1-2 x) y'(x)+4 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1619

\((1-2 x) (1-x) y''(x)+2 (3-4 x) y'(x)+12 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1620

\(2 (x+1)^2 y''(x)-(x+1) y'(x)+y(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1621

\(2 (x+1)^2 y''(x)-(x+1) y'(x)+y(x)=x\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1622

\(4 x^2 y''(x)+y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1623

\(4 x^2 y''(x)+y(x)=\sqrt {x}\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1624

\(y(x) \left (4 k x-4 p^2-x^2+1\right )+4 x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1625

\(\left (4 a^2 x^2+1\right ) y(x)+4 x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1626

\(-\left (a^2-x\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1627

\(4 x^2 y''(x)-\left (4 x^2+1\right ) y(x)+4 x y'(x)=4 e^x x^{3/2}\)

[[_2nd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1628

\(-\left ((2 n+1)^2-4 x^2\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1629

\(-\left (a^2 x^2+1\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1630

\(4 x^2 y''(x)-8 x y'(x)+5 y(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1631

\(4 x^2 y''(x)-2 (x+2) x y'(x)+(x+3) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1632

\(4 x^2 y''(x)-\left (-4 x^2+4 x+1\right ) y(x)+4 (1-2 x) x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1633

\(4 x^3 y'(x)+4 x^2 y''(x)-\left (3-2 x^2\right ) y(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1634

\(4 x^3 y'(x)+4 x^2 y''(x)+\left (x^4+2 x^2+1\right ) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1635

\(\left (a+x^4+2 x^2\right ) y(x)+4 x^3 y'(x)+4 x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1636

\(4 \left (1-x^2\right ) y''(x)-8 x y'(x)-y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1637

\(-\left (4 p^2+1\right ) y(x)+4 \left (1-x^2\right ) y''(x)-8 x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1638

\(4 \left (x^2+1\right ) y''(x)=x^2+4 x y'(x)\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1639

\(4 a x y'(x)-a (a+2) y(x)+4 \left (1-x^2\right ) y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1640

\(4 (1-x) x y''(x)+2 (1-x) y'(x)+y(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1641

\(y(x) (a+b x)+4 (1-x) x y''(x)+2 (1-2 x) y'(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1642

\(y(x) \left (a+b x+c x^2\right )+4 (1-x) x y''(x)+2 (1-2 x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1643

\(y(x) \left (\sum _{m=0}^n a(m) x^m\right )+4 (1-x) x y''(x)+2 (1-2 x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1644

\(-(k-p) (k+p+1) y(x)+2 (1-(3-2 k) x) y'(x)+4 (1-x) x y''(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1645

\(2 (a x+1) y'(x)+y(x) \left (b+k^2 x\right )+4 (1-x) x y''(x)=0\)

[_Jacobi]

Solution method TO DO

Maple
Mathematica

ODE 1646

\((2 x+1)^2 y''(x)-2 (2 x+1) y'(x)-12 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1647

\((2 x+1)^2 y''(x)-2 (2 x+1) y'(x)-12 y(x)=3 x+1\)

[[_2nd_order, _exact, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1648

\((1-3 x)^2 y''(x)-3 (1-3 x) y'(x)-9 y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1649

\(16 x^2 y''(x)+(4 x+3) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1650

\(16 x^2 y''(x)+32 x y'(x)-(4 x+5) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1651

\(\left (a x^2+1\right ) y''(x)+a x y'(x)+b^2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1652

\(\left (a x^2+1\right ) y''(x)+b x y'(x)+c y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1653

\(\left (1-a^2 x^2\right ) y''(x)-2 a^2 x y'(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1654

\(\left (1-a^2 x^2\right ) y''(x)-2 a^2 x y'(x)+2 a^2 y(x)=0\)

[_Gegenbauer]

Solution method TO DO

Maple
Mathematica

ODE 1655

\(x (a+b x) y''(x)+2 a y'(x)-2 b y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1656

\(y''(x) \left (\text {a0}+\text {b0} x+\text {c0} x^2\right )+(\text {a1}+\text {b1} x) y'(x)+2 \text {a2} y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1657

\(\text {a1} (a+b x) y'(x)+(a+b x)^2 y''(x)+\text {a2} y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1658

\(x^3 y''(x)=a+b x\)

[[_2nd_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 1659

\(x^3 y''(x)+x y'(x)-y(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1660

\(x^3 y''(x)+x y'(x)-2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1661

\(x^3 y''(x)+2 x y'(x)-y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1662

\(\text {a1} x y'(x)+y(x) (\text {a2}+\text {b2} x)+x^3 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1663

\(y(x) \left (a+b x+c x^2\right )+x^3 y''(x)+x^2 y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1664

\(x^3 y''(x)+3 x^2 y'(x)+x y(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1665

\(x^3 y''(x)+3 x^2 y'(x)+x y(x)=1\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1666

\(a x^2 y'(x)+y(x) (b+c x)+x^3 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1667

\(\left (\text {a1}+\text {b1} x^2\right ) y'(x)+\text {a2} x y(x)+x^3 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1668

\(x (\text {a1}+\text {b1} x) y'(x)+\text {a2} y(x)+x^3 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1669

\(x (\text {a1}+\text {b1} x) y'(x)+y(x) (\text {a2}+\text {b2} x)+x^3 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1670

\(\left (1-x^3\right ) y''(x)+6 x y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1671

\(x \left (1-x^2\right ) y''(x)-y'(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1672

\(x^3+\left (1-x^2\right ) x y''(x)-y'(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1673

\(a x^3 y(x)+\left (1-x^2\right ) x y''(x)-y'(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1674

\(x \left (1-x^2\right ) y''(x)-\left (x^2+7\right ) y'(x)+4 x y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1675

\(x \left (x^2+1\right ) y''(x)-2 \left (x^2+1\right ) y'(x)+2 x y(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1676

\(x \left (x^2+1\right ) y''(x)-2 \left (1-x^2\right ) y'(x)-2 x y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1677

\(x \left (1-x^2\right ) y''(x)-2 \left (1-x^2\right ) y'(x)-2 x y(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1678

\(\left (a+b x^2\right ) y'(x)+c x y(x)+x \left (x^2+1\right ) y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1679

\(\left (a+b x^2\right ) y'(x)+(a-1) x (a+b) y(x)+x \left (1-x^2\right ) y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1680

\(\left (a+b x^2\right ) y'(x)+2 (1-b) x y(x)+x \left (1-x^2\right ) y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1681

\(\left (a-(a+1) x^2\right ) y'(x)+c x y(x)+x \left (1-x^2\right ) y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1682

\(\left (a+b x^2\right ) y'(x)+c x y(x)+x \left (1-x^2\right ) y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1683

\(x \left (x^2+2\right ) y''(x)-y'(x)-6 x y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1684

\(x \left (2-x^2\right ) y''(x)-\left (x^2+4 x+2\right ) y(x)-\left (-x^3-3 x^2+2 x+2\right ) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1685

\(x \left (\text {a0}+x^2\right ) y''(x)+\left (\text {a1}+\text {b1} x^2\right ) y'(x)+\text {a2} x y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1686

\(x^2 (x+1) y''(x)+x y'(x)+(x+1)^3 (-y(x))=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1687

\((1-x) x^2 y''(x)-(x+1) x y'(x)+y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1688

\((x+1) x^2 y''(x)-(2 x+1) x y'(x)+(2 x+1) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1689

\((1-x) x^2 y''(x)+2 (2-x) x y'(x)+2 (x+1) y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1690

\((1-x) x^2 y''(x)-(4-5 x) x y'(x)+(6-9 x) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1691

\((x+1) x^2 y''(x)+2 (3 x+2) x y'(x)+2 (3 x+1) y(x)=0\)

[[_2nd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 1692

\(x (\text {a1}+\text {b1} x) y'(x)+y(x) (\text {a2}+\text {b2} x)+(1-x) x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1693

\(x^2 (\text {a0}+x) y''(x)+x (\text {a1}+\text {b1} x) y'(x)+y(x) (\text {a2}+\text {b2} x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1694

\((1-x)^2 x y''(x)-2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1695

\(x \left (x^2+1\right ) y''(x)+x (x+1) y'(x)+y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1696

\(x (2-x)^2 y''(x)+2 (2-x) y'(x)+2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1697

\((1-x) x (a-x) y''(x)+y'(x) \left (x^2 (\text {a0}+\text {a1}+1)+\text {a0} \text {a2}-\text {a0}+\text {a1}+x (\text {a2}+\text {a3})-\text {a3}+1\right )+\text {a0} \text {a1} (x-k) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1698

\((\text {a1}-x) (\text {a2}-x) (\text {a3}-x) y''(x)+y'(x) \left (\text {b0}+\text {b1} x+\text {b2} x^2\right )+y(x) (\text {c0}+\text {c1} x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1699

\(\left (1-2 x^3\right ) y''(x)+6 x^2 y'(x)-6 x y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1700

\(2 (1-x) x^2 y''(x)+(3-5 x) x y'(x)-(x+1) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1701

\(2 (2-x) x^2 y''(x)-(4-x) x y'(x)+(3-x) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1702

\(x \left (3 x^2+1\right ) y''(x)+2 y'(x)-6 x y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1703

\(4 (x+1) x^2 y''(x)-4 x^2 y'(x)+(3 x+1) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1704

\(x^2 (a+b x) y''(x)-2 x (2 a+b x) y'(x)+2 y(x) (3 a+b x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1705

\(y(x) (a+b x)+4 (1-x) x y''(x)+2 (1-3 x) (1-x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1706

\(4 (1-x) x (1-a x) y''(x)+y'(x) \left (\text {a0}+\text {a1} x+\text {a2} x^2\right )+y(x) \left (\text {b0}+\text {b1} x^2\right )=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1707

\(a^2 y(x)+x^4 y''(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1708

\(x^4 y''(x)+\left (1-2 x^2\right ) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1709

\(x^4 y''(x)-\left (2 x^2+1\right ) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1710

\(\left (e^{2/x}-a^2\right ) y(x)+x^4 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1711

\(x^4 y''(x)+x y'(x)-2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1712

\(x^4 y''(x)-2 x^2 y'(x)+(2 x+1) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1713

\(x^4 y''(x)+x^3 y'(x)+y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1714

\(x^4 y''(x)+x^3 y'(x)-(x+1) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1715

\(y(x) \left (a+b x^2+c x^4\right )+x^4 y''(x)+x^3 y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1716

\(x^4 y''(x)+\left (x^2+1\right ) x y'(x)+y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1717

\(x^4 y''(x)-\left (1-x^2\right ) x y'(x)+\left (1-x^2\right ) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1718

\(a^2 y(x)+x^4 y''(x)+2 x^3 y'(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1719

\(x^4 y''(x)+\left (2 x^2+1\right ) x y'(x)-y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1720

\(2 x^2 (a+x) y'(x)+b y(x)+x^4 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1721

\(\left (x^3+1\right ) x y''(x)-\left (1-x^3\right ) y'(x)+x^2 (-y(x))=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1722

\(x^3 \left (-y'(x)\right )+\left (1-x^2\right ) x^2 y''(x)-2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1723

\(\left (1-x^2\right ) x^2 y''(x)-\left (2-x^2\right ) x y'(x)+\left (2-x^2\right ) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1724

\(a (a+1) y(x)-2 x^3 y'(x)+\left (1-x^2\right ) x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1725

\(\left (x^2+1\right )^2 y''(x)+2 x \left (x^2+1\right ) y'(x)+y(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1726

\(\left (x^2+1\right )^2 y''(x)+2 x \left (x^2+1\right ) y'(x)+4 y(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1727

\(a^2 (-y(x))+\left (x^2+1\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1728

\(-y(x) \left (m^2-n (n+1) \left (1-x^2\right )\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1729

\(-y(x) \left (k^2-p (p+1) \left (1-x^2\right )\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1730

\(-y(x) \left (a^2-k \left (1-x^2\right )\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1731

\(y(x) \left (\text {a0}+\text {a2} x^2+\text {a4} x^4\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1732

\(y(x) \left (\sum _{m=0}^n a(m) x^m\right )+\left (1-x^2\right )^2 y''(x)-2 x \left (1-x^2\right ) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1733

\(a x \left (1-x^2\right ) y'(x)+b y(x)+\left (x^2+1\right )^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1734

\(\text {a1} x \left (1-x^2\right ) y'(x)+y(x) \left (\text {a2}+\text {b2} x+\text {c2} x^2\right )+\left (1-x^2\right )^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1735

\(x^2 \left (a^2+x^2\right )^2 y''(x)+x \left (a^2+2 x^2\right ) y'(x)+b^2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1736

\(\left (a^2+x^2\right )^2 y''(x)+2 x \left (a^2+2 x^2\right ) y'(x)-y(x) \left (\text {a0}+\text {a2} x^2+\text {a4} x^4\right )=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1737

\(\left (a^2-x^2\right )^2 y''(x)-2 x \left (a^2-x^2\right ) y'(x)+y(x) \left (\text {a0}+\text {a2} x^2+\text {a4} x^4\right )=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1738

\(\left (a^2+x^2\right )^2 \left (b^2+x^2\right ) y''(x)+x \left (\text {a0}+\text {b0} x^2\right ) y'(x)+y(x) \left (\text {a1}+\text {b1} x^2\right )=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1739

\(\left (a^2-x^2\right )^2 \left (b^2-x^2\right ) y''(x)+x \left (\text {a0}+\text {b0} x^2\right ) y'(x)+y(x) \left (\text {a1}+\text {b1} x^2+\text {c1} x^4\right )=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1740

\((1-x) x (x+1)^2 y''(x)+2 (3-x) x (x+1) y'(x)-2 (1-x) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1741

\(y(x) \left (a+b x+c x^2\right )+(1-x)^2 x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1742

\((1-x)^2 x^2 y''(x)+(1-2 x) (1-x) x y'(x)-y(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1743

\((1-x) x (\text {a1}+\text {b2} x) y'(x)+y(x) \left (\text {a2}+\text {b2} x+\text {c2} x^2\right )+(1-x)^2 x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1744

\(y(x) \left (\sum _{m=0}^n a(m) x^m\right )+(1-x)^2 x^2 y''(x)+(1-2 x) (1-x) x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1745

\(x^2 (a-x)^2 y''(x)+b y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1746

\((a-x)^2 (b-x)^2 y''(x)=k^2 y(x)\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1747

\((a-x) (A+2 x) (b-x) y'(x)+(a-x)^2 (b-x)^2 y''(x)+B y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1748

\((a-x)^4 y''(x)-2 (a-x)^3 y'(x)-y(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1749

\((1-2 x) (1-x) x^2 y''(x)+2 (2-3 x) x y'(x)+2 (3 x+1) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1750

\((1-2 x) (1-x) x^2 y''(x)+2 (1-2 x) (2-x) x y'(x)+2 (1-x) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1751

\(-y(x) \left (4 k^2+\left (4 p^2+1\right ) \left (1-x^2\right )\right )+4 \left (1-x^2\right )^2 y''(x)-8 x \left (1-x^2\right ) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1752

\(-y(x) \left (4 k^2+\left (1-4 p^2\right ) \left (1-x^2\right )\right )+4 \left (1-x^2\right )^2 y''(x)-8 x \left (1-x^2\right ) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1753

\(-y(x) \left (a (a+1) (1-x)+b^2 x\right )+4 \left (1-x^2\right ) x^2 y''(x)+2 (1-3 x) (1-x) x y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1754

\((a+b x)^4 y''(x)+y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1755

\(y''(x) \left (a+b x+c x^2\right )^2+A y(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1756

\(x^5 y''(x)+x y'(x)-y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1757

\(x^5 y''(x)-\left (1-2 x^3\right ) x y'(x)+\left (1-2 x^3\right ) y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1758

\(x \left (a^2-x^2\right ) \left (b^2-x^2\right ) y''(x)+\left (\text {a0}+\text {b0} x^4\right ) y'(x)+x^3 y(x) \left (\text {a1}+\text {b1} x^2+\text {c1} x^4\right )=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1759

\(a y(x)+x^6 y''(x)-x^5 y'(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1760

\(x^6 y''(x)+3 x^5 y'(x)+y(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1761

\(x^3 \left (a+3 x^2\right ) y'(x)+x^6 y''(x)+y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1762

\((a-x) (b-x) (c-x) y'(x) \left (\text {a1}+\text {b1} x+\text {c1} x^2\right )+(a-x)^2 (b-x)^2 (c-x)^2 y''(x)+y(x) \left (\text {a2}+\text {b2} x+\text {c2} x^2\right )=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1763

\(4 x^6 y''(x)+\left (1-2 x^2\right ) y(x)+4 \left (2 x^2+1\right ) x^3 y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1764

\(4 x^6 y''(x)+\left (8 x^4+10 x^2+1\right ) y(x)-4 \left (2 x^2+1\right ) x^3 y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1765

\(\left (4 b-a^2\right ) y(x)+4 x^6 y''(x)+12 x^5 y'(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1766

\(x^{2 a} y''(x)+a x^{2 a-1} y'(x)+(1-a)^2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Solution method TO DO

Maple
Mathematica

ODE 1767

\(a^2 x^{a-1} y(x)+x^{a+1} y''(x)+(1-2 a) x^a y'(x)=0\)

[[_Emden, _Fowler]]

Solution method TO DO

Maple
Mathematica

ODE 1768

\(x^2 y''(x) \left (\text {a0}+\text {b0} x^k\right )+x y'(x) \left (\text {a1}+\text {b1} x^k\right )+y(x) \left (\text {a2}+\text {b2} x^k\right )=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1769

\(\left (1-a^2 \cos ^2(x)\right ) y''(x)+a^2 \sin (x) \cos (x) y'(x)+y(x) \left (\text {a0}+\text {a1} \cos ^2(x)\right )=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1770

\(-y(x) \left (4 k^2-\left (1-p^2\right ) \sinh ^2(x)\right )+4 \sinh ^2(x) y''(x)+4 \sinh (x) \cosh (x) y'(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1771

\(y''(x)=0\)

[[_2nd_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 1772

\(y''(x)=a y(x)\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1773

\(y''(x)=6 y(x)^2\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1774

\(y''(x)=6 y(x)^2+x\)

[[_Painleve, `1st`]]

Solution method TO DO

Maple
Mathematica

ODE 1775

\(y''(x)=a+b x+c y(x)^2\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1776

\(y''(x)=2 y(x)^3\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1777

\(y''(x)=a+b y(x)+2 y(x)^3\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1778

\(y''(x)=a+2 y(x)^3+x y(x)\)

[[_Painleve, `2nd`]]

Solution method TO DO

Maple
Mathematica

ODE 1779

\(y''(x)=f(x)+g(x) y(x)+2 y(x)^3\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1780

\(y''(x)=-2 a b x y(x)+a+2 b^2 y(x)^3\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1781

\(y''(x)=\text {a0}+\text {a1} x y(x)+\text {a2} y(x)+\text {a3} y(x)^3\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1782

\(y''(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2+\text {a3} y(x)^3\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1783

\(a x^r y(x)^s+y''(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1784

\(a \sin (y(x))+y''(x)=0\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1785

\(a e^{y(x)}+y''(x)=0\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1786

\(y''(x)=f(y(x))\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1787

\(y(x) \left (f'(x)+2 f(x)^2\right )+3 f(x) y'(x)+y''(x)=2 y(x)^3\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 1788

\(y''(x)+y(x) y'(x)=0\)

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1789

\(y''(x)+y(x) y'(x)=y(x)^3\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1790

\(a y(x)+y''(x)+y(x) y'(x)=y(x)^3\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1791

\(y''(x)+y(x) y'(x)=12 f'(x)-12 f(x) y(x)+y(x)^3\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 1792

\(2 a^2 y(x)+(3 a+y(x)) y'(x)+a y(x)^2+y''(x)=y(x)^3\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1793

\(y''(x)=y(x) \left (f'(x)-2 f(x)^2\right )+(3 f(x)-y(x)) y'(x)+f(x) y(x)^2+y(x)^3\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 1794

\(y''(x)=(3 \text {f1}(x)-y(x)) y'(x)+\text {f1}(x) y(x)^2+\text {f2}(x)+\text {f3}(x) y(x)+y(x)^3\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1795

\(y''(x)=y'(x) (\text {f0}(x) y(x)+\text {f1}(x))+\text {g0}(x) y(x)^3+\text {g1}(x) y(x)^2+\text {g2}(x) y(x)+\text {g3}(x)\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1796

\(y''(x)=y(x) f'(x)+(f(x)-2 y(x)) y'(x)\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 1797

\(y''(x)=(f(x)-2 y(x)) y'(x)+f(x) y(x)^2+g(x)\)

[[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1798

\(y''(x)=(\text {f1}(x)-2 y(x)) y'(x)+\text {f2}(x) y(x)^2+\text {f3}(x)\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1799

\(y''(x)=(\text {f1}(x)-2 y(x)) y'(x)+\text {f2}(x) y(x)^2+\text {f3}(x) y(x)+\text {f4}(x)\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1800

\(y''(x)=a+4 b^2 y(x)+3 b y(x)^2+3 y(x) y'(x)\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1801

\(y''(x)+3 y(x) y'(x)=f(x)+g(x) y(x)-y(x)^3\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1802

\(y''(x)=(f(x)-3 y(x)) y'(x)+f(x) y(x)^2-y(x)^3\)

[[_2nd_order, _with_potential_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1803

\(y''(x)=a \left (2 y(x) y'(x)+1\right )\)

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1804

\(a \left (y(x)^2-1\right ) y'(x)+b y(x)+y''(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1805

\(y'(x) f(x,y(x))+g(x,y(x))+y''(x)=0\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1806

\(y''(x)=\left (x^2-y'(x)\right )^2+2 x\)

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1807

\(y''(x)+2 y'(x)^2 \tan (y(x))+2 \cot (x) y'(x)=0\)

[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1808

\(y''(x)=a y'(x)^2\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1809

\(y''(x)=a^2+b^2 y'(x)^2\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1810

\(a y'(x)^2+b y(x)+y''(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1811

\(a y'(x)^2+b \sin (y(x))+y''(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1812

\(a y'(x)^2+b y'(x)+c y(x)+y''(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1813

\(y''(x)=e^x y'(x)^2\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1814

\(f(x) y'(x)+g(x) y'(x)^2+y''(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1815

\(a y(x) y'(x)^2+b y(x)+y''(x)=0\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1816

\(f(y(x)) y'(x)^2+g(y(x))+y''(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1817

\(f(x) y'(x)+g(y(x)) y'(x)^2+y''(x)=0\)

[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1818

\(f(y(x)) y'(x)+g(y(x)) y'(x)^2+y''(x)=0\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1819

\(f(y(x)) y'(x)+g(y(x)) y'(x)^2+h(y(x))+y''(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1820

\(y''(x)+y'(x)^3+y'(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1821

\(y''(x)=(a-x) y'(x)^3\)

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1822

\(y''(x)+\left (e^{2 y(x)}+x\right ) y'(x)^3=0\)

[[_2nd_order, _with_exponential_symmetries], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1823

\(y''(x)+4 y'(x)^3+2 y'(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1824

\(a y'(x)^3+y''(x)=0\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1825

\(y''(x)=x y'(x)^3\)

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1826

\(y'(x)^3 (a x+b y(x))+y''(x)=0\)

[[_2nd_order, _with_exponential_symmetries], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1827

\(a y(x) \left (y'(x)^2+1\right )^2+y''(x)=0\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1828

\(y''(x)=a \left (x y'(x)-y(x)\right )^k\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1829

\(f(x) y'(x)^k+g(x) y'(x)+y''(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1830

\(y''(x)=A x^a y(x)^b y'(x)^c\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1831

\(y''(x)=a \sqrt {y'(x)^2+1}\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1832

\(y''(x)=a \sqrt {b y(x)^2+y'(x)^2}\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1833

\(y''(x)=a \left (y'(x)^2+1\right )^{3/2}\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1834

\(y''(x)=a x \left (y'(x)^2+1\right )^{3/2}\)

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1835

\(y''(x)=a y(x) \left (y'(x)^2+1\right )^{3/2}\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1836

\(y''(x)=a y(x) \left (\left (b-y'(x)\right )^2+1\right )^{3/2}\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1837

\(y''(x)=a \left (y'(x)^2+1\right )^{3/2} (b+c x+y(x))\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1838

\(y''(x)+y(x)^3 y'(x)=y(x) y'(x) \sqrt {4 y'(x)+y(x)^4}\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1839

\(y''(x)=f\left (y'(x)\right )\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1840

\(y''(x)=f\left (a x+b y(x),y'(x)\right )\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1841

\(y''(x)=y(x) f\left (x,\frac {y'(x)}{y(x)}\right )\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1842

\(y''(x)=x^{n-2} f\left (x^{-n} y(x),x^{1-n} y'(x)\right )\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1843

\(2 y''(x)=12 y(x)^2+1\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1844

\(2 y''(x)=y(x) \left (a-y(x)^2\right )\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1845

\(8 y''(x)+9 y'(x)^4=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1846

\(a x e^{y(x)}+x y''(x)+y'(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1847

\(x y''(x)+2 y'(x)+x y(x)^5=0\)

[_Emden, [_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1848

\(x y(x)^n+x y''(x)+2 y'(x)=0\)

[_Emden, [_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1849

\(x^m y(x)^n+x y''(x)+2 y'(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1850

\(a x^m y(x)^n+x y''(x)+2 y'(x)=0\)

[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1851

\(a y'(x)+b x e^{y(x)}+x y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1852

\(\left (2-a x^2\right ) y'(x)+x y''(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1853

\(x y''(x)=(1-y(x)) y'(x)\)

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1854

\(x y''(x)+x y'(x)^2=y'(x)\)

[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1855

\(x y''(x)=x y'(x)^2+y'(x)\)

[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1856

\(x y''(x)+2 x y'(x)^2-2 y'(x)=0\)

[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1857

\(x y''(x)=x^2 y'(x)^2-2 y'(x)-y(x)^2\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1858

\(a x^2 y'(x)^2+x y''(x)+2 y'(x)=b\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1859

\(\left (a x y'(x)-y(x)\right )^2+x y''(x)=b\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1860

\(x y''(x)=y'(x)^3+y'(x)\)

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1861

\(x y''(x)+2 y'(x)=a x^{2 k} y'(x)^k\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1862

\(2 x y''(x)+y'(x)^3+y'(x)=0\)

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1863

\(a y(x) \left (1-y(x)^n\right )+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1864

\(a e^{y(x)-1}+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1865

\((a+1) x y'(x)+x^2 y''(x)=x^k f\left (x^k y(x),k y(x)+x y'(x)\right )\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1866

\(x^2 y''(x)+y'(x)^2=0\)

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1867

\(x^2 y''(x)=\left (3 x-2 y'(x)\right ) y'(x)\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1868

\(x^2 y''(x)+x^2 y'(x)^2+4 x y'(x)+2=0\)

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1869

\(x^2 y''(x)=x^4 y'(x)^2-4 x^2 y(x)^2+6 y(x)\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1870

\(a \left (x y'(x)-y(x)\right )^2+x^2 y''(x)=b x^2\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1871

\(a x^4 y'(x)^2+x^2 y''(x)+2 x y(x)=b\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1872

\(a y(x) y'(x)^2+b x+x^2 y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1873

\(x^2 y''(x)=\sqrt {a x^2 y'(x)^2+b y(x)^2}\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1874

\(x^2 y''(x)=y(x) f\left (\frac {x y'(x)}{y(x)}\right )\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1875

\(\left (x^2+1\right ) y''(x)+y'(x)^2+1=0\)

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1876

\(a y(x)^3+9 x^2 y''(x)+2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1877

\(x^3 y''(x)-x^2 y'(x)=3-x^2\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 1878

\(x^3 \left (y''(x)+y(x) y'(x)-y(x)^3\right )+12 x y(x)+24=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1879

\(x^3 y''(x)=a \left (x y'(x)-y(x)\right )^2\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1880

\(2 x^3 y''(x)+x^2 (2 x y(x)+9) y'(x)+x y(x) \left (-2 x^2 y(x)^2+3 x y(x)+12\right )-6=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1881

\(x^4 y''(x)=x \left (x^2+2 y(x)\right ) y'(x)-4 y(x)^2\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1882

\(x^4 y''(x)=x^2 y'(x) \left (y'(x)+x\right )-4 y(x)^2\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1883

\(x^4 y''(x)+\left (x y'(x)-y(x)\right )^3=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1884

\(x^a y''(x)+y(x)^b=0\)

[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1885

\(\left (1-12 x^2\right ) \left (3 y'(x)+y(x)^2\right )+2 x \left (1-4 x^2\right ) \left (y''(x)+y(x) y'(x)-y(x)^3\right )-48 x y(x)+24=0\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1886

\(a x y(x)+b-\left (k x^{k-1}-12 x^2\right ) \left (3 y'(x)+y(x)^2\right )+2 \left (x^k-4 x^3\right ) \left (y''(x)+y(x) y'(x)-y(x)^3\right )=0\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1887

\(\sqrt {x} y''(x)=y(x)^{3/2}\)

[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1888

\(x^{3/2} y''(x)=f\left (\frac {y(x)}{\sqrt {x}}\right )\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1889

\(y''(x) \left (a+2 b x+c x^2\right )^{3/2}=f\left (\frac {x}{\sqrt {a+2 b x+c x^2}}\right )\)

[[_2nd_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 1890

\(f(x) f'(x) y'(x)+f(x)^2 y''(x)=g\left (y(x),f(x) y'(x)\right )\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 1891

\(f(x)^2 y''(x)=y'(x) \left (3 f(x) f'(x)-f(x)^2 y(x)+3 f(x)^3\right )-24 f(x)^4\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 1892

\(f(x)^2 y''(x)=-a f(x)^5+3 f(x) f'(x)-f(x)^2 y(x)+3 f(x)^3\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 1893

\(2 f(x)^2 y''(x)=f(x) y'(x) \left (3 f'(x)-2 f(x) y(x)\right )+f(x) y(x)^2 f'(x)+y(x) \left (f(x) f''(x)-2 f'(x)^2-2 f(x)^3\right )+2 f(x)^2 y(x)^3\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 1894

\(y(x) y''(x)=a\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1895

\(y(x) y''(x)=y'(x)^2\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1896

\(y(x) y''(x)+y'(x)^2=0\)

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1897

\(y(x) y''(x)=y'(x)^2-a^2\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1898

\(y(x) y''(x)+y'(x)^2=a^2\)

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1899

\(y(x) y''(x)+y'(x)^2+y(x)^2=0\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1900

\(2 a^2 y(x)^2+y(x) y''(x)+y'(x)^2=0\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1901

\(y(x) y''(x)=\text {a0}+\text {a1} y(x)+y(x)^3 (\text {a2}+\text {a3} y(x))+y'(x)^2\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1902

\(y(x) y''(x)=\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2+\text {a3} y(x)^3+\text {a4} y(x)^4+y'(x)^2\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1903

\(y(x) y''(x)=y'(x)^2+y(x) y'(x)\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1904

\(y(x) y''(x)=e^x y(x) \left (\text {a0}+\text {a1} y(x)^2\right )+e^{2 x} \left (\text {a2}+\text {a3} y(x)^4\right )+y'(x)^2\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1905

\(y(x) y''(x)=y'(x)^2+y(x)^2 \log (y(x))\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1906

\(y(x) y''(x)=-x^2 y(x)^2+y'(x)^2+y(x)^2 \log (y(x))\)

[[_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1907

\(y(x) y''(x)+y'(x)^2=y'(x)\)

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1908

\(y(x) y''(x)=y'(x)^2-y'(x)\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1909

\(y(x) y''(x)=y(x)^2 \left (f(x) y(x)+g'(x)\right )+y'(x)^2+y'(x)\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 1910

\(y(x) y''(x)=y'(x)^2-2 y'(x)\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1911

\(y(x) y''(x)+y'(x)^2-x y'(x)+y(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1912

\(a x y'(x)+y(x) y''(x)+y'(x)^2=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1913

\(y(x) y''(x)=-y(x) f'(x)+f(x) y'(x)+y'(x)^2+y(x)^3\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 1914

\(y(x) y''(x)=y(x) f''(x)-f(x) y'(x)-f(x) y(x)^3+y'(x)^2+y(x)^4\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 1915

\(y(x) y''(x)=-a y(x) y'(x)-b y(x)^2+y'(x)^2\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1916

\(y(x) y''(x)=a y(x) y'(x)+b y(x)^2+y'(x)^2+y(x)^3\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1917

\(y(x) y''(x)=y(x)^2 y'(x)+y'(x)^2\)

[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1918

\(y(x) y''(x)=f(x) y(x) y'(x)+g(x) y(x)^2+y'(x)^2\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1919

\(y(x) y''(x)=-y(x) \left (f'(x)-y(x)^2 g'(x)\right )+y'(x) \left (f(x)+g(x) y(x)^2\right )+y'(x)^2\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 1920

\(y(x) y''(x)=2 y'(x)^2+y(x)^2\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1921

\(y(x) y''(x)=2 \left (y'(x)^2-y(x)^2\right )\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1922

\(y(x) y''(x)=-3 y(x) y'(x)+3 y'(x)^2+y(x)^2\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1923

\(y(x) y''(x)=a y'(x)^2\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1924

\(y(x) y''(x)=a y'(x)^2+b\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1925

\(y(x) y''(x)=a y'(x)^2+b y(x)^3\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1926

\(y(x) y''(x)=a y'(x)^2+\text {a0}+\text {a1} y(x)+\text {a2} y(x)^2+\text {a3} y(x)^3+\text {a3} y(x)^2+\text {a4} y(x)^4\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1927

\(y(x) y''(x)=a y'(x)^2+b y(x) y'(x)+c y(x)^2\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1928

\(y(x) y''(x)=\text {a3} y(x)^{a+1}+a y'(x)^2+\text {a1} y(x) y'(x)+\text {a2} y(x)^2\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1929

\(a y'(x)^2+f(x) y(x) y'(x)+g(x) y(x)^2+y(x) y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1930

\(y(x) y''(x)+y'(x)^3=0\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1931

\(y(x) y''(x)+y'(x)^3-y'(x)^2=0\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1932

\(y(x) y''(x)=y'(x)^2 \left (y'(x) (-\sin (y(x)))-y(x) y'(x) \cos (y(x))+1\right )\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1933

\((1-y(x)) y''(x)+2 y'(x)^2=0\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1934

\((a+y(x)) y''(x)=y'(x)^2\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1935

\((a+y(x)) y''(x)+y'(x)^2=b\)

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1936

\((a+y(x)) y''(x)+b y'(x)^2=0\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1937

\((y(x)+x) y''(x)+y'(x)^2-y'(x)=0\)

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1938

\((x-y(x)) y''(x)+2 y'(x) \left (y'(x)+1\right )=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1939

\((x-y(x)) y''(x)=\left (y'(x)+1\right ) \left (y'(x)^2+1\right )\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1940

\((x-y(x)) y''(x)=f\left (y'(x)\right )\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1941

\(2 y(x) y''(x)=y'(x)^2\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1942

\(2 y(x) y''(x)+y'(x)^2+1=0\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1943

\(2 y(x) y''(x)=a+y'(x)^2\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1944

\(2 y(x) y''(x)=y'(x)^2+8 y(x)^3\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1945

\(2 y(x) y''(x)=y'(x)^2+8 y(x)^3+4 y(x)^2\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1946

\(2 y(x) y''(x)=y'(x)^2+4 (2 y(x)+x) y(x)^2\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1947

\(2 y(x) y''(x)=y(x)^2 (a+b y(x))+y'(x)^2\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1948

\(2 y(x) y''(x)=a y(x)^3+y'(x)^2-2 x y(x)^2-1\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1949

\(2 y(x) y''(x)=y(x)^2 (a x+b y(x))+y'(x)^2\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1950

\(2 y(x) y''(x)=y'(x)^2+3 y(x)^4\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1951

\(2 y(x) y''(x)=-a^2-4 \left (b-x^2\right ) y(x)^2+y'(x)^2+3 y(x)^4+8 x y(x)^3\)

[[_Painleve, `4th`]]

Solution method TO DO

Maple
Mathematica

ODE 1952

\(2 y(x) y''(x)=-2 y(x)^2 \left (f'(x)+f(x)^2\right )-3 f(x) y(x) y'(x)+y'(x)^2+8 y(x)^3\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 1953

\(2 y(x) y''(x)=2 x f(x) y(x)^2-4 y(x)^2 y'(x)+y'(x)^2-y(x)^4-1\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 1954

\(2 y(x) y''(x)=3 y'(x)^2\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1955

\(2 y(x) y''(x)=3 y'(x)^2+4 y(x)^2\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1956

\(2 y(x) y''(x)=f(x) y(x)^2+3 y'(x)^2\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1957

\(2 y(x) y''(x)=6 y'(x)^2+\left (1-3 y(x)^2\right ) y(x)^2\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1958

\(2 y(x) y''(x)=6 y'(x)^2-y(x)^2 \left (a y(x)^3+1\right )\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1959

\(2 y(x) y''(x)=y'(x)^2 \left (y'(x)^2+1\right )\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 1960

\(3 y(x) y''(x)=2 y'(x)^2+36 y(x)^2\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1961

\(3 y(x) y''(x)=5 y'(x)^2\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1962

\(4 y(x) y''(x)=3 y'(x)^2-4 y(x)\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1963

\(4 y(x) y''(x)=3 y'(x)^2+12 y(x)^2\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1964

\(4 y(x) y''(x)=a y(x)+b y(x)^2+c y(x)^3+3 y'(x)^2\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1965

\(5 y(x) y''(x)=y'(x)^2\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1966

\(12 y(x) y''(x)=15 y'(x)^2-8 y(x)^3\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 1967

\(a y(x) y''(x)=(a-1) y'(x)^2\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1968

\(a (a+2)^2 y(x) y''(x)=a^2 (a+2) y(x)^3 f'(x)-a^2 f(x)^2 y(x)^4+a (a+2)^2 f(x) y(x)^2 y'(x)+(a-1) (a+2)^2 y'(x)^2\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 1969

\(x y(x) y''(x)+x y'(x)^2+y(x) y'(x)=0\)

[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1970

\(x y(x) y''(x)+x y'(x)^2=y(x) y'(x)\)

[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1971

\(x y(x) y''(x)=x y'(x)^2-y(x) y'(x)\)

[_Liouville, [_Painleve, `3rd`], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1972

\(x y(x) y''(x)=x \left (\text {a0}+\text {a1} y(x)^4\right )+y(x) \left (\text {a2}+\text {a3} y(x)^2\right )+x y'(x)^2-y(x) y'(x)\)

[[_Painleve, `3rd`]]

Solution method TO DO

Maple
Mathematica

ODE 1973

\(x y(x) y''(x)+x y'(x)^2+2 y(x) y'(x)=0\)

[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1974

\(x y(x) y''(x)+x y'(x)^2=3 y(x) y'(x)\)

[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1975

\(a y(x) y'(x)+f(x)+x y(x) y''(x)+x y'(x)^2=0\)

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1976

\(x y(x) y''(x)=a y(x) y'(x)+x y'(x)^2+x y(x)^3\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1977

\(x y(x) y''(x)=a y(x) y'(x)+b^2 x y(x)^3+x y'(x)^2\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 1978

\(x y(x) y''(x)+2 x y'(x)^2+y(x) y'(x)=0\)

[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1979

\(x y(x) y''(x)-2 x y'(x)^2+y(x) y'(x)=0\)

[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1980

\(x y(x) y''(x)-2 x y'(x)^2-y(x) y'(x)=0\)

[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1981

\(x y(x) y''(x)=2 x y'(x)^2-(y(x)+1) y'(x)\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1982

\(a y(x) y'(x)+x y(x) y''(x)+2 x y'(x)^2=0\)

[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1983

\(a y(x) y'(x)+x y(x) y''(x)-2 x y'(x)^2=0\)

[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1984

\(x y(x) y''(x)-4 x y'(x)^2+4 y(x) y'(x)=0\)

[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1985

\(a y'(x) \left (x y'(x)-y(x)\right )+x y(x) y''(x)=0\)

[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1986

\(x (y(x)+x) y''(x)+x y'(x)^2+(x-y(x)) y'(x)=y(x)\)

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1987

\(2 x y(x) y''(x)=x y'(x)^2-y(x) y'(x)\)

[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1988

\(x^2+x (2 y(x)+x) y''(x)+2 x y'(x)^2+4 (y(x)+x) y'(x)+2 y(x)=0\)

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1989

\(x^2 y(x) y''(x)+\left (x y'(x)-y(x)\right )^2=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1990

\(x^2 y(x) y''(x)+\left (x y'(x)-y(x)\right )^2=3 y(x)^2\)

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1991

\(x^2 y(x) y''(x)=a x y(x) y'(x)+a y(x)^2+2 x^2 y'(x)^2\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1992

\(a x^2 y'(x)^2+b x y(x) y'(x)+c y(x)^2+x^2 y(x) y''(x)\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1993

\(x^2 (1-y(x)) y''(x)+2 x^2 y'(x)^2-2 x (1-y(x)) y'(x)+2 (1-y(x))^2 y(x)=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1994

\(x^2 (x-y(x)) y''(x)=\left (x y'(x)-y(x)\right )^2\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1995

\(x^2 (x-y(x)) y''(x)+\left (x y'(x)-y(x)\right )^2=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1996

\(x^2 (x-y(x)) y''(x)=a \left (x y'(x)-y(x)\right )^2\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1997

\(2 x^2 y(x) y''(x)=x^2 y'(x)^2-y(x)^2\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1998

\(2 x^2 y(x) y''(x)=x^2 y'(x)^2+2 x y(x) y'(x)-4 y(x)^2\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 1999

\(x^3 y(x) y''(x)+x^3 y'(x)^2+6 x^2 y(x) y'(x)+3 x y(x)^2=a\)

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2000

\(x (x+1)^2 y(x) y''(x)=a (x+2) y(x)^2-2 \left (x^2+1\right ) y(x) y'(x)+x (x+1)^2 y'(x)^2\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2001

\(8 \left (1-x^3\right ) y(x) y''(x)+4 \left (1-x^3\right ) y'(x)^2-12 x^2 y(x) y'(x)+3 x y(x)^2=0\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2002

\(\sqrt {a^2+x^2} \left (b y'(x)^2+y(x) y''(x)\right )=y(x) y'(x)\)

[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2003

\(\sqrt {a^2-x^2} \left (x y(x) y''(x)-x y'(x)^2-y(x) y'(x)\right )=b x y'(x)^2\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2004

\(\text {f0}(x) y(x) y''(x)+\text {f1}(x) y'(x)^2+\text {f2}(x) y(x) y'(x)+\text {f3}(x) y(x)^2=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2005

\(4 f(x) y(x) y''(x)=y'(x) \left (2 f'(x)-6 f(x) y(x)^2\right )+2 y(x)^3 f'(x)+3 f(x) g(x) y(x)^2+3 f(x) y'(x)^2-f(x) y(x)^4+4 f(x)^2 y(x)\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2006

\(y(x)^2 y''(x)=a\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 2007

\(a x+y(x)^2 y''(x)+y(x) y'(x)^2=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2008

\(y(x)^2 y''(x)+y(x) y'(x)^2=a+b x\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2009

\(\left (y(x)^2+1\right ) y''(x)+(1-2 y(x)) y'(x)^2=0\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2010

\(\left (y(x)^2+1\right ) y''(x)=3 y(x) y'(x)^2\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2011

\(\left (y(x)^2+1\right ) y''(x)=(a+3 y(x)) y'(x)^2\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2012

\(\left (y(x)^2+1\right ) y''(x)+y'(x) \left (y'(x)^2+1\right )=0\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 2013

\(\left (y(x)^2+x\right ) y''(x)+2 y(x) y'(x)^2+2 y'(x)=a\)

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2014

\(\left (y(x)^2+x\right ) y''(x)=2 \left (x-y(x)^2\right ) y'(x)^3-y'(x) \left (4 y(x) y'(x)+1\right )\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 2015

\(\left (x^2+y(x)^2\right ) y''(x)=\left (y(x)^2+1\right ) \left (x y'(x)-y(x)\right )\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 2016

\(\left (x^2+y(x)^2\right ) y''(x)=2 \left (y(x)^2+1\right ) \left (x y'(x)-y(x)\right )\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 2017

\(2 (1-y(x)) y(x) y''(x)=(1-2 y(x)) y'(x)^2\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2018

\(2 (1-y(x)) y(x) y''(x)=f(x) (1-y(x)) y(x) y'(x)+(1-2 y(x)) y'(x)^2\)

[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2019

\(2 (1-y(x)) y(x) y''(x)=(1-3 y(x)) y'(x)^2\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2020

\(2 (1-y(x)) y(x) y''(x)=4 y(x) y'(x) (f(x)+g(x) y(x))+(1-3 y(x)) y'(x)^2\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 2021

\(2 (1-y(x)) y(x) y''(x)=-4 y(x)^2 (1-y(x)) \left (f'(x)+f(x)^2+g'(x)-g(x)^2\right )-4 y(x) y'(x) (f(x)+g(x) y(x))+(1-y(x))^3 \left (-\left (\text {F0}(x)^2-\text {G0}(x)^2 y(x)^2\right )\right )+(1-3 y(x)) y'(x)^2\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2022

\(3 (1-y(x)) y(x) y''(x)=2 (1-2 y(x)) y'(x)^2\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2023

\(4 (1-y(x)) y(x) y''(x)=3 (1-2 y(x)) y'(x)^2\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2024

\(x y(x)^2 y''(x)=a\)

[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2025

\(x y(x)^2 y''(x)=\left (a-y(x)^2\right ) y'(x)+x y(x) y'(x)^2\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2026

\(x^2 y(x)^2 y''(x)=\left (x^2+y(x)^2\right ) \left (x y'(x)-y(x)\right )\)

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2027

\(\left (a^2-x^2\right ) \left (a^2-y(x)^2\right ) y''(x)+\left (a^2-x^2\right ) y(x) y'(x)^2=x \left (a^2-y(x)^2\right ) y'(x)\)

[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2028

\((1-y(x))^3 \left (\text {a0}+\text {a1} y(x)^2\right )+\text {a2} x (1-y(x)) y(x)^2+\text {a3} x^3 y(x)^2 (y(x)+1)+2 x^2 (1-y(x)) y(x) y''(x)-x^2 (1-3 y(x)) y'(x)^2+2 x (1-y(x)) y(x) y'(x)=0\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 2029

\(x^3 y(x)^2 y''(x)+(y(x)+x) \left (x y'(x)-y(x)\right )^3=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2030

\(y(x)^3 y''(x)=a^2\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 2031

\(y(x) \left (y(x)^2+1\right ) y''(x)+\left (1-3 y(x)^2\right ) y'(x)^2=0\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2032

\(2 y(x)^3 y''(x)+y(x)^2 y'(x)^2=2\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2033

\(2 (1-y(x)) y(x) (a-y(x)) y''(x)+(-(1-y(x)) (a-y(x))+y(x) (a-y(x))+(1-y(x)) y(x)) y'(x)^2=\text {a0} y(x)^2 \left (1-y(x)^2\right ) (a-y(x))^2+\text {a2} y(x)^2 (a-y(x))^2+\text {a3} (1-y(x))^2 (a-y(x))^2+\text {a1} (1-y(x))^2 y(x)^2\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2034

\(2 (a-y(x)) (b-y(x)) (c-y(x)) y''(x)+y'(x)^2 ((a-y(x)) (b-y(x))+(a-y(x)) (c-y(x))+(b-y(x)) (c-y(x)))=\text {a0} (a-y(x))^2 (b-y(x))^2 (c-y(x))^2+2 \text {a2} (a-y(x))^2 (c-y(x))^2+\text {a3} (a-y(x))^2 (b-y(x))^2+\text {a1} (b-y(x))^2 (c-y(x))^2\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2035

\(2 (1-x) x (1-y(x)) (x-y(x)) y(x) y''(x)=2 (1-y(x)) \left (x^2-2 x y(x)+y(x)\right ) y(x) y'(x)+(1-x) x \left (3 y(x)^2-2 x y(x)-2 y(x)+x\right ) y'(x)^2-\left (1-y(x)^2\right ) y(x)^2\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 2036

\(2 (1-x) x (1-y(x)) (x-y(x)) y(x) y''(x)=f(x) ((1-y(x)) (x-y(x)) y(x))^{3/2}+2 (1-y(x)) \left (x^2-2 x y(x)+y(x)\right ) y(x) y'(x)+(1-x) x \left (3 y(x)^2-2 x y(x)-2 y(x)+x\right ) y'(x)^2-\left (1-y(x)^2\right ) y(x)^2\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2037

\(2 (1-x)^2 x^2 (1-y(x)) (x-y(x)) y(x) y''(x)=\text {a0} x (x-y(x))^2 (1-y(x))^2+\text {a1} (1-x) (x-y(x))^2 y(x)^2+(\text {a2}-1) (1-x) x y(x)^2 (1-y(x))^2+\text {a3} (x-y(x))^2 y(x)^2 (1-y(x))^2+2 (1-x) x y(x) \left (x^2-2 x y(x)+y(x)\right ) (1-y(x))^2 y'(x)+(1-x)^2 x^2 \left (3 y(x)^2-2 x y(x)-2 y(x)+x\right ) y'(x)^2\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 2038

\(b \sqrt {\left (1-y(x)^2\right ) \left (1-a^2 y(x)^2\right )} y'(x)^2+\left (1-y(x)^2\right ) \left (1-a^2 y(x)^2\right ) y''(x)+y(x) \left (-2 a^2 y(x)^2+a^2+1\right )=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2039

\(a^2 y(x)+\left (x^2+y(x)^2\right )^2 y''(x)=0\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 2040

\(y''(x) \left (a+2 b x+c x^2+y(x)^2\right )^2+A y(x)=0\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 2041

\(\text {f0}(y(x)) y''(x)+\text {f1}(y(x)) y'(x)^2+\text {f2}(y(x)) y'(x)+\text {f3}(y(x))=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2042

\(\sqrt {y(x)} y''(x)=a\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 2043

\(\sqrt {y(x)} y''(x)=2 (a+b x)\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2044

\(y''(x) X(x,y(x))^3=1\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 2045

\(y''(x) \left (\text {a0}+\text {a1} \sin ^2(y(x))\right )+\text {a2} y(x) \left (\text {a1} \sin ^2(y(x))+\text {a3}\right )+\text {a1} y'(x)^2+\text {a1} y'(x)^2 \sin (y(x)) \cos (y(x))=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2046

\(y(x) y''(x) (1-\log (y(x)))+y'(x)^2 (\log (y(x))+1)=0\)

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

Solution method TO DO

Maple
Mathematica

ODE 2047

\(f(y(x)) y''(x)=y'(x)^2 f'(y(x))-g(x) f(y(x)) y'(x)-h(x) f(y(x))^2\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2048

\(f(y(x)) y''(x)=f(y(x))^2 \text {F0}\left (x,\frac {y'(x)}{f(y(x))}\right )+y'(x)^2 f'(y(x))\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2049

\(a y'(x)^2 f'(y(x))+f(y(x)) y''(x)+g(y(x))=0\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2050

\(y'(x) y''(x)=a^2 x\)

[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]

Solution method TO DO

Maple
Mathematica

ODE 2051

\(y'(x) y''(x)=x^2 y(x) y'(x)+x y(x)^2\)

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]

Solution method TO DO

Maple
Mathematica

ODE 2052

\(\left (2 x^2 y'(x)+y(x)^2\right ) y''(x)+2 (y(x)+x) y'(x)^2+x y'(x)+y(x)=0\)

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]]

Solution method TO DO

Maple
Mathematica

ODE 2053

\(a y(x)^2+x^3 y'(x) y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2054

\(\text {f1} y'(x) y''(x)+\text {f2} y(x) y''(x)+\text {f3} y'(x)^2+\text {f4} y(x) y'(x)+\text {f5} y(x)^2=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2055

\(3 y(x) y'(x) y''(x)=y'(x)^3-1\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 2056

\(\left (x^2+2 y(x)^2 y'(x)\right ) y''(x)+2 y(x) y'(x)^3+3 x y'(x)+y(x)=0\)

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]]

Solution method TO DO

Maple
Mathematica

ODE 2057

\(\left (x-y'(x)^2\right ) y''(x)=x^2-y'(x)\)

[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]]

Solution method TO DO

Maple
Mathematica

ODE 2058

\(\left (y'(x)^2+y(x)^2\right ) y''(x)+y(x)^3=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2059

\(y''(x) \left (a \left (x y'(x)-y(x)\right )+y'(x)^2\right )=b\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2060

\(4 y(x) y'(x)^2 y''(x)=y'(x)^4+3\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 2061

\(y''(x) f\left (y'(x)\right )+g(y(x)) y'(x)+h(x)=0\)

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 2062

\(y''(x)^2=a+b y(x)\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 2063

\(y''(x)^2=a+b y'(x)^2\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2064

\(y''(x)^2-x y''(x)+y'(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2065

\(a^2 y''(x)^2=\left (y'(x)^2+1\right )^3\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2066

\(a x+x y''(x)^2-2 y'(x) y''(x)=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2067

\(\left (x y''(x)-y'(x)\right )^2=y''(x)^2+1\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2068

\(2 \left (x^2+1\right ) y''(x)^2+2 \left (x-y'(x)\right ) y'(x)-x \left (4 y'(x)+x\right ) y''(x)=2 y(x)\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 2069

\(3 x^2 y''(x)^2+4 y'(x)^2-2 \left (3 x y'(x)+y(x)\right ) y''(x)=0\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2070

\((2-9 x) x^2 y''(x)^2+6 y(x) y''(x)-6 (1-6 x) x y'(x) y''(x)=36 x y'(x)^2\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2071

\(\text {f0} y''(x)^2+\text {f1} y'(x) y''(x)+\text {f2} y(x) y''(x)+\text {g0} y'(x)^2+\text {g1} y(x) y'(x)+h y(x)^2=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2072

\(y(x) y''(x)+4 y(x) y'(x)^3-y'(x)^2=0\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]]

Solution method TO DO

Maple
Mathematica

ODE 2073

\(\left (y(x) y''(x)+y'(x)^2+1\right )^2=\left (y'(x)^2+1\right )^3\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 2074

\(y''(x)^2 \left (a^2-b^2 y(x)^2\right )+y'(x)^2 \left (1-b^2 y'(x)^2\right )+2 b^2 y(x) y'(x)^2 y''(x)=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2075

\(\left (x^2 y(x) y''(x)+x^2 \left (-y'(x)^2\right )+y(x)^2\right )^2=4 x y(x) \left (x y'(x)-y(x)\right )^3\)

[[_2nd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2076

\(y''(x)^3=12 y'(x) \left (x y''(x)-2 y'(x)\right )\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2077

\(32 y''(x) \left (x y''(x)-y'(x)\right )^3+\left (2 y(x) y''(x)-y'(x)^2\right )^3=0\)

type_of_ode

Solution method TO DO

Maple
Mathematica

ODE 2078

\(f\left (y''(x)\right )+x y''(x)=y'(x)\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2079

\(y'(x) f\left (\frac {y''(x)}{y'(x)}\right )=y'(x)^2-y(x) y''(x)\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2080

\(f\left (y''(x),y'(x)-x y''(x),\frac {1}{2} x^2 y''(x)-x y'(x)+y(x)\right )=0\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 2081

\(f\left (x,y''(x)\right )=0\)

[[_2nd_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 2082

\(f\left (y(x),y''(x)\right )=0\)

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Solution method TO DO

Maple
Mathematica

ODE 2083

\(f\left (y'(x),y''(x)\right )=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2084

\(f\left (x,y'(x),y''(x)\right )=0\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2085

\(f\left (y(x),y'(x),y''(x)\right )=0\)

[[_2nd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2086

\(y'''(x)=0\)

[[_3rd_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 2087

\(y'''(x)=\cos (x)+1\)

[[_3rd_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 2088

\(y'''(x)+\sin (x)=0\)

[[_3rd_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 2089

\(y'''(x)=\sin ^3(x)\)

[[_3rd_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 2090

\(y'''(x)=y(x)\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2091

\(y'''(x)=x^2+y(x)\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2092

\(y'''(x)=y(x)+e^x x+\cos ^2(x)\)

[[_3rd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2093

\(y'''(x)+a y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2094

\(y'''(x)=x y(x)\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2095

\(y'''(x)+y'(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2096

\(y'''(x)=y'(x)\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2097

\(y'''(x)+y'(x)=x^3+\cos (x)\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2098

\(y'''(x)-2 y'(x)+4 y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2099

\(y'''(x)-2 y'(x)+4 y(x)=e^x \cos (x)\)

[[_3rd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2100

\(y'''(x)-3 y'(x)+2 y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2101

\(y'''(x)-3 y'(x)+2 y(x)=3 e^x\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2102

\(y'''(x)-3 y'(x)+2 y(x)=e^x x^2\)

[[_3rd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2103

\(y'''(x)-4 y'(x)=x^2-3 e^{2 x}\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2104

\(y'''(x)-7 y'(x)+6 y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2105

\(y'''(x)=a^2 y(x)\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2106

\(y'''(x)+2 x y'(x)+y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2107

\(y'''(x)+2 a x y'(x)+a y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2108

\(y'''(x)+y(x) f'(x)+2 f(x) y'(x)=0\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2109

\(y'''(x)-y''(x)+y'(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2110

\(y'''(x)-y''(x)+y'(x)+y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2111

\(y'''(x)+y''(x)+y'(x)-3 y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2112

\(y'''(x)-y''(x)-2 y'(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2113

\(y'''(x)-y''(x)-2 y'(x)=e^{-x}\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2114

\(y'''(x)+y''(x)+4 y'(x)+4 y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2115

\(y'''(x)+y''(x)+2 y'(x)+4 y(x)=\sin (2 x)\)

[[_3rd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2116

\(y'''(x)+y''(x)-7 y'(x)-15 y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2117

\(y'''(x)+2 y''(x)+y'(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2118

\(y'''(x)+2 y''(x)+y'(x)=(x-1) x\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2119

\(y'''(x)-2 y''(x)+y'(x)=e^x\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2120

\(y'''(x)-2 y''(x)-y'(x)+2 y(x)=\sinh (x)\)

[[_3rd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2121

\(y'''(x)-2 y''(x)-3 y'(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2122

\(y'''(x)-2 y''(x)-3 y'(x)=3 x^2+\sin (x)\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2123

\(y'''(x)-2 y''(x)-3 y'(x)=3 x^2+e^{-x}\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2124

\(y'''(x)-2 y''(x)+3 y'(x)+10 y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2125

\(y'''(x)-a^2 y'(x)+2 a^2 y(x)-2 y''(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2126

\(y'''(x)-a^2 y'(x)+2 a^2 y(x)-2 y''(x)=\sinh (x)\)

[[_3rd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2127

\(y'''(x)-3 y''(x)+4 y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2128

\(y'''(x)+3 y''(x)-y'(x)-3 y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2129

\(y'''(x)-3 y''(x)-y'(x)+3 y(x)=x^2\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2130

\(y'''(x)+3 y''(x)-y'(x)-3 y(x)=\cosh (x)\)

[[_3rd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2131

\(y'''(x)+3 y''(x)+3 y'(x)+y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2132

\(y'''(x)+3 y''(x)+3 y'(x)+y(x)=e^{-x} x\)

[[_3rd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2133

\(y'''(x)-3 y''(x)+3 y'(x)-y(x)=x \left (1-e^x x^2\right )\)

[[_3rd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2134

\(y'''(x)+3 y''(x)+3 y'(x)+y(x)=e^{-x} \left (2-x^2\right )\)

[[_3rd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2135

\(y'''(x)-3 y''(x)+4 y'(x)-2 y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2136

\(y'''(x)-3 y''(x)+4 y'(x)-2 y(x)=e^x+\cos (x)\)

[[_3rd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2137

\(y'''(x)-4 y''(x)+5 y'(x)-2 y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2138

\(y'''(x)-4 y''(x)+5 y'(x)-2 y(x)=x\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2139

\(y'''(x)-4 y''(x)+6 y'(x)-4 y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2140

\(y'''(x)-6 y''(x)+9 y'(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2141

\(y'''(x)-6 y''(x)+12 y'(x)-8 y(x)=e^{2 x} x^2\)

[[_3rd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2142

\(y'''(x)+a^3 (-y(x))+3 a^2 y'(x)-3 a y''(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2143

\(y'''(x)+a^3 (-y(x))+3 a^2 y'(x)-3 a y''(x)=e^{a x}\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2144

\(y'''(x)=a y''(x)\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2145

\(y'''(x)+\text {a1} y''(x)+\text {a2} y'(x)+\text {a3} y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2146

\(y'''(x)-2 \left (-2 a-4 x^2+1\right ) y'(x)-8 a x y(x)-6 x y''(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2147

\(y'''(x)+a^3 x^3 y(x)+3 a^2 x^2 y'(x)+3 a x y''(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2148

\(y'''(x)+x^2 \left (-y''(x)\right )+2 x y'(x)-2 y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2149

\(y'''(x)+y''(x) (2 \cot (x)+\csc (x))-y'(x)=\cot (x)\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2150

\(y'''(x)-\sin (x) y''(x)-2 \cos (x) y'(x)+y(x) \sin (x)=\log (x)\)

[[_3rd_order, _fully, _exact, _linear]]

Solution method TO DO

Maple
Mathematica

ODE 2151

\(y'''(x)+y'(x) \left (2 f'(x)^2+f'(x)+4 g(x)\right )+2 y(x) \left (2 f(x) g(x)+g'(x)\right )+3 f(x) y''(x)=0\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2152

\(y'''(x)+f(x) y''(x)+f(x) y(x)+y'(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2153

\(4 y'''(x)-3 y'(x)+y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2154

\(4 y'''(x)-8 y''(x)-11 y'(x)-3 y(x)=0\)

[[_3rd_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2155

\(4 y'''(x)-8 y''(x)-11 y'(x)-3 y(x)+18 e^x=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2156

\(x y'''(x)=2\)

[[_3rd_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 2157

\(x y'''(x)+3 y'(x)+x y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2158

\(x y'''(x)-y''(x)+x y'(x)-y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2159

\(x y'''(x)-y''(x)-x y'(x)+y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2160

\(x y'''(x)-y''(x)-x y'(x)+y(x)=1-x^2\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2161

\(x y'''(x)+x^2 (-y(x))+3 y''(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2162

\(x y'''(x)-\left (3-x^2\right ) y''(x)+4 x y'(x)+2 y(x)=0\)

[[_3rd_order, _fully, _exact, _linear]]

Solution method TO DO

Maple
Mathematica

ODE 2163

\((1-2 x) y'''(x)-(x+4) y''(x)-2 y'(x)=0\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2164

\(x^2 y'''(x)+a x^2 y(x)-6 y'(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2165

\(x^2 y'''(x)+2 x y''(x)=a\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2166

\(x^2 y'''(x)+\left (x^2+2\right ) y'(x)+4 x y''(x)+3 x y(x)=f(x)\)

[[_3rd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2167

\(x^2 y'''(x)+5 x y''(x)+4 y'(x)=\log (x)\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2168

\(x^2 y'''(x)+6 x y''(x)+6 y'(x)=0\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2169

\(x^2 y'''(x)+a x^2 y(x)+6 x y''(x)+6 y'(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2170

\(x^2 y'''(x)-2 (n+1) x y''(x)+6 n y'(x)=0\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2171

\(x^2 y'''(x)+\left (6-2 x^3\right ) y'(x)+2 x^3 y(x)+\left (6-x^2\right ) x y''(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2172

\(\left (x^2+1\right ) y'''(x)+8 x y'(x)+10 y'(x)=0\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2173

\(\left (x^2+2\right ) y'''(x)+\left (x^2+2\right ) y'(x)-2 x y''(x)-2 x y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2174

\(\left (x^2-2 x+2\right ) y'''(x)+x^2 \left (-y''(x)\right )+2 x y'(x)-2 y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2175

\((x+2)^2 y'''(x)+(x+2) y''(x)+y'(x)=0\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2176

\(4 x^2 y'''(x)+8 x y''(x)+y'(x)=0\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2177

\(x (\text {a0}+\text {b0} x) y'''(x)+(\text {a1}+\text {b1} x) y''(x)+x y'(x)+y(x)=f(x)\)

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2178

\(x^3 y'''(x)=a\)

[[_3rd_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 2179

\(x^3 y'''(x)+x y'(x)-y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2180

\(x^3 y'''(x)+x y'(x)-y(x)=x \log (x)\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2181

\(x^3 y'''(x)-x^2 y''(x)+2 x y'(x)-2 y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2182

\(x^3 y'''(x)-x^2 y''(x)+2 x y'(x)-2 y(x)=x \left (x^2+3\right )\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2183

\(x^3 y'''(x)+x^2 y''(x)+3 x y'(x)-8 y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2184

\(x^3 y'''(x)-x^2 y''(x)+x y'(x)=0\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2185

\(x^3 y'''(x)+2 x^2 y''(x)+2 y(x)=0\)

[[_3rd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2186

\(x^3 y'''(x)+2 x^2 y''(x)-x y'(x)+y(x)=0\)

[[_3rd_order, _exact, _linear, _homogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2187

\(x^3 y'''(x)+3 x^2 y''(x)=a\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2188

\(x^3 y'''(x)+3 x^2 y''(x)-2 x y'(x)+2 y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2189

\(x^3 y'''(x)-3 x^2 y''(x)+7 x y'(x)-8 y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2190

\(x^3 y'''(x)+\left (1-a^2\right ) x y'(x)+3 x^2 y''(x)=0\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2191

\(x^3 y'''(x)+4 x^2 y''(x)-8 x y'(x)+8 y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2192

\(x^3 y'''(x)-4 x^2 y''(x)+\left (x^2+8\right ) x y'(x)-2 \left (x^2+4\right ) y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2193

\(x^3 y'''(x)-\left (12-a x^3\right ) y(x)+6 x^2 y''(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2194

\(x^3 y'''(x)+x^2 \log (x) y''(x)+2 x y'(x)-y(x)=2 x^3\)

[[_3rd_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2195

\(\left (x^3+1\right ) y'''(x)+9 x^2 y''(x)+18 x y'(x)+6 y(x)=0\)

[[_3rd_order, _fully, _exact, _linear]]

Solution method TO DO

Maple
Mathematica

ODE 2196

\(x \left (x^2+1\right ) y'''(x)+3 \left (2 x^2+1\right ) y''(x)-12 y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2197

\(x \left (1-x^2\right ) y'''(x)+\left (3-8 x^2\right ) y''(x)-14 x y'(x)-4 y(x)=0\)

[[_3rd_order, _fully, _exact, _linear]]

Solution method TO DO

Maple
Mathematica

ODE 2198

\(x \left (x^2-2 x+2\right ) y'''(x)+\left (-x^3+3 x^2-6 x+6\right ) y''(x)=0\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2199

\((x+1)^3 y'''(x)+(x+1)^2 y''(x)+3 (x+1) y'(x)-8 y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2200

\(x^2 (y(x)+3) y'''(x)-3 (x+2) x y''(x)+6 (x+1) y'(x)-6 y(x)=0\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 2201

\(4 x^3 y'''(x)+x y'(x)-y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2202

\((1-2 x)^3 y'''(x)+(1-2 x) y'(x)+2 y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2203

\(x^4 y'''(x)+2 x^3 y''(x)+2 x y(x)=10 \left (x^2+1\right )\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2204

\(x^4 y'''(x)+2 x^3 y''(x)-x^2 y'(x)+x y(x)=1\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2205

\(\left (x^2+1\right ) x^2 y'''(x)+8 x^3 y''(x)+10 x^2 y'(x)=3 x^2+2 x^2 \log (x)-1\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2206

\((x+1) x^3 y'''(x)-2 (2 x+1) x^2 y''(x)+2 (5 x+2) x y'(x)-4 (3 x+1) y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2207

\(4 x^4 y'''(x)-4 x^3 y''(x)+4 x^2 y'(x)=1\)

[[_3rd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2208

\(\left (x^2+1\right ) x^3 y'''(x)-2 \left (2 x^2+1\right ) x^2 y''(x)+2 \left (5 x^2+2\right ) x y'(x)-4 \left (3 x^2+1\right ) y(x)=0\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2209

\((a-x)^3 (b-x)^3 y'''(x)=c y(x)\)

[[_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2210

\((x+\sin (x)) y'''(x)+3 (\cos (x)+1) y''(x)-3 \sin (x) y'(x)-y(x) \cos (x)+\sin (x)=0\)

[[_3rd_order, _fully, _exact, _linear]]

Solution method TO DO

Maple
Mathematica

ODE 2211

\(y''''(x)=0\)

[[_high_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 2212

\(y''''(x)=x \cos (x)\)

[[_high_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 2213

\(y''''(x)+4 e^{-x} \cos (x)=0\)

[[_high_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 2214

\(y''''(x)=y(x)+\cos (x)\)

[[_high_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2215

\(y''''(x)=y(x)+e^x \cos (x)\)

[[_high_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2216

\(y''''(x)+a y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2217

\(y''''(x)=a^4 y(x)+x^3\)

[[_high_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2218

\(y''''(x)+y''(x)+y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2219

\(y''''(x)+2 y''(x)+y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2220

\(y''''(x)-2 y''(x)+y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2221

\(y''''(x)+2 y''(x)+y(x)=\cos (x)\)

[[_high_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2222

\(y''''(x)-2 y''(x)+y(x)=\cos (x)\)

[[_high_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2223

\(y''''(x)+2 y''(x)+y(x)=24 x \sin (x)\)

[[_high_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2224

\(y''''(x)-2 y''(x)+y(x)=e^x+4\)

[[_high_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2225

\(y''''(x)-2 y''(x)-8 y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2226

\(y''''(x)+3 y''(x)-4 y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2227

\(y''''(x)+5 y''(x)+6 y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2228

\(y''''(x)-12 y''(x)+27 y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2229

\(y''''(x)+a^2 y''(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2230

\(y''''(x)+a^4 y(x)+2 a^2 y''(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2231

\(y''''(x)+a^4 y(x)+2 a^2 y''(x)=\cosh (a x)\)

[[_high_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2232

\(y''''(x)+\left (a^2+b^2\right ) y''(x)+a^2 b^2 y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2233

\(y''''(x)+3 y(x) \left (f''(x)+3 f(x)^2\right )+10 f'(x) y'(x)+10 f(x) y''(x)=0\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2234

\(-y'''(x)+y''''(x)-3 y''(x)+5 y'(x)-2 y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2235

\(-y'''(x)+y''''(x)-3 y''(x)+5 y'(x)-2 y(x)=e^{3 x}\)

[[_high_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2236

\(-2 y'''(x)+y''''(x)+y(x)^2=0\)

[[_high_order, _missing_x], [_high_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2237

\(-2 y'''(x)+y''''(x)+y(x)^2=x^3\)

[NONE]

Solution method TO DO

Maple
Mathematica

ODE 2238

\(2 y'''(x)+y''''(x)-2 y'(x)-y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2239

\(-2 y'''(x)+y''''(x)+2 y''(x)-2 y'(x)+y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2240

\(2 y'''(x)+y''''(x)+3 y''(x)+2 y'(x)+y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2241

\(2 y'''(x)+y''''(x)-3 y''(x)-4 y'(x)+4 y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2242

\(-3 y'''(x)+y''''(x)+y''(x)-y'(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2243

\(-4 y'''(x)+y''''(x)+6 y''(x)-4 y'(x)+y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2244

\(-4 y'''(x)+y''''(x)+12 y''(x)-16 y'(x)+16 y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2245

\(4 a x y'''(x)+y''''(x)+a^4 x^4 y(x)+4 a^3 x^3 y'(x)+6 a^2 x^2 y''(x)=0\)

[[_high_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2246

\(2 \left (y''''(x)+\left (a^2+b^2\right ) y''(x)+a^2 b^2 y(x)\right )=\cos (a x)+\cos (b x)\)

[[_high_order, _linear, _nonhomogeneous]]

Solution method TO DO

Maple
Mathematica

ODE 2247

\(-12 y'''(x)+4 y''''(x)+11 y''(x)-3 y'(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2248

\(3 y'''(x)+x y''''(x)=0\)

[[_high_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2249

\(5 y'''(x)+x y''''(x)=0\)

[[_high_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2250

\(x^2 y''''(x)=2 y'''(x)\)

[[_high_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2251

\(x^2 y''''(x)=2 y''(x)\)

[[_high_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2252

\(x^2 y''''(x)+4 x y'''(x)+2 y''(x)=0\)

[[_high_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2253

\(x^2 y''''(x)+6 x y'''(x)+6 y''(x)=0\)

[[_high_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2254

\(x^2 y''''(x)+8 x y'''(x)+12 y''(x)=0\)

[[_high_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2255

\(x^2 y''''(x)+8 x y'''(x)+a^2 (-y(x))+12 y''(x)=0\)

[[_high_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2256

\((a+x)^2 y''''(x)=1\)

[[_high_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 2257

\(32 x (a-b+2) y'''(x)+16 x^2 y''''(x)+16 (a-b+1) (a-b+2) y''(x)+c^4 (-y(x))=0\)

[[_high_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2258

\(x^3 y''''(x)+2 x^2 y'''(x)+a^4 \left (-x^3\right ) y(x)-x y''(x)=0\)

[[_high_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2259

\(x^3 y''''(x)+6 x^2 y'''(x)+6 x y''(x)=0\)

[[_high_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2260

\(x^2 (a+b+c+3) y'''(x)+x^3 y''''(x)+x (a b+a c+a+b c+b+c+1) y''(x)-y'(x) (x-a b c)-k y(x)=0\)

[[_high_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2261

\(x^4 y''''(x)+6 x^3 y'''(x)+4 x^2 y''(x)-2 x y'(x)-4 y(x)=0\)

[[_high_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2262

\(x^4 y''''(x)+6 x^3 y'''(x)+9 x^2 y''(x)+3 x y'(x)+y(x)=0\)

[[_high_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2263

\(x^4 y''''(x)+8 x^3 y'''(x)+12 x^2 y''(x)=0\)

[[_high_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2264

\(x^4 y''''(x)+8 x^3 y'''(x)+a y(x)+12 x^2 y''(x)=0\)

[[_high_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2265

\(\text {A1} x^3 y'''(x)+x^4 y''''(x)+\text {A2} x^2 y''(x)+\text {A3} x y'(x)+\text {A4} y(x)=0\)

[[_high_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2266

\(16 a^4 x^4 y''''(x)-32 (1-2 a) a^2 x^3 y'''(x)+16 (1-2 a) (1-a) a^2 x^2 y''(x)-b^4 x^{2/a} y(x)=0\)

[[_high_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2267

\(4 \left (e^x+2\right ) y'''(x)+\left (2 x+e^x\right ) y''''(x)+6 e^x y''(x)+4 e^x y'(x)+e^x y(x)=0\)

[[_high_order, _fully, _exact, _linear]]

Solution method TO DO

Maple
Mathematica

ODE 2268

\(-y'''(x)+y'''''(x)-2 y''(x)+2 y'(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2269

\(2 y'''(x)+y'''''(x)+y'(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2270

\(2 y'''(x)+y'''''(x)+y'(x)=a x+b \cos (x)+c \sin (x)\)

[[_high_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2271

\(y''''''(x)=0\)

[[_high_order, _quadrature]]

Solution method TO DO

Maple
Mathematica

ODE 2272

\(y''''''(x)+a y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2273

\(2 y'''(x)+y''''''(x)+y(x)=0\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2274

\(y''''''''(x)=y(x)\)

[[_high_order, _missing_x]]

Solution method TO DO

Maple
Mathematica

ODE 2275

\(y''''''''(x)-2 y''''+y(x)=0\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2276

\(y^{(2 n)}(x)=a^{2 n} y(x)\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2277

\(x^n y^{(2 n)}(x)=y(x)\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2278

\(x^{n+\frac {1}{2}} y^{(2 n+1)}(x)=y(x)\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2279

\(y^{(n)}(x)=e^x x\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2280

\(a m x^{m-1} y(x)+a x^m y'(x)+y^{(n)}(x)=0\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2281

\((a-x)^n (b-x)^n y^{(n)}(x)=c y(x)\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2282

\(y'''(x)=y'(x) \left (y'(x)+1\right )\)

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

Solution method TO DO

Maple
Mathematica

ODE 2283

\(y'''(x)+y'(x)^2-y(x) y'(x)=0\)

[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2284

\(y'''(x)+a y(x) y''(x)=0\)

[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2285

\(x^2 y'''(x)+x y''(x)-(1-2 x y(x)) y'(x)+y(x)^2=f(x)\)

[[_3rd_order, _exact, _nonlinear]]

Solution method TO DO

Maple
Mathematica

ODE 2286

\(x^2 y'''(x)-x (1-y(x)) y''(x)+x y'(x)^2+(1-y(x)) y'(x)=0\)

[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

Solution method TO DO

Maple
Mathematica

ODE 2287

\(y(x) y'''(x)+y(x)^3 y'(x)-y'(x) y''(x)=0\)

[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2288

\((a+y(x)) y'''(x)+3 y'(x) y''(x)=0\)

[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

Solution method TO DO

Maple
Mathematica

ODE 2289

\(x^3 y(x) y'''(x)+3 x^3 y'(x) y''(x)+9 x^2 y(x) y''(x)+9 x^2 y'(x)^2+18 x y(x) y'(x)+3 y(x)^2=0\)

[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2290

\(\left (y(x)^2+x\right ) y'''(x)+3 y''(x)+2 y'(x)^3+6 y(x) y'(x) y''(x)=0\)

[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2291

\(4 y(x)^2 y'''(x)+15 y'(x)^3-18 y(x) y'(x) y''(x)=0\)

[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2292

\(9 y(x)^2 y'''(x)+40 y'(x)^3-45 y(x) y'(x) y''(x)=0\)

[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2293

\(y'(x) y'''(x)+y'(x)^2=2 y''(x)^2\)

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2294

\(y'(x) y''(x)=a x y'(x)^5+3 y''(x)^2\)

[[_2nd_order, _missing_y]]

Solution method TO DO

Maple
Mathematica

ODE 2295

\(2 y'(x) y'''(x)=2 y''(x)^2\)

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

Solution method TO DO

Maple
Mathematica

ODE 2296

\(\left (y'(x)^2+1\right ) y'''(x)=3 y'(x) y''(x)^2\)

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

Solution method TO DO

Maple
Mathematica

ODE 2297

\(\left (y'(x)^2+1\right ) y'''(x)=y''(x)^2 \left (a+3 y'(x)\right )\)

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

Solution method TO DO

Maple
Mathematica

ODE 2298

\(y'(x)^3 y'''(x)=1\)

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

Solution method TO DO

Maple
Mathematica

ODE 2299

\(y''(x) y'''(x)=2\)

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

Solution method TO DO

Maple
Mathematica

ODE 2300

\(y''(x) y'''(x)=a \sqrt {b^2 y''(x)^2+1}\)

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

Solution method TO DO

Maple
Mathematica

ODE 2301

\(2 x y''(x) y'''(x)=y''(x)^2-a^2\)

[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

Solution method TO DO

Maple
Mathematica

ODE 2302

\(\left (1-x^2\right ) \left (y'''(x)\right )^2+2 x y''(x) y'''(x)-y''(x)^2+1=0\)

[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2303

\(\sqrt {y''(x)^2+1} \left (1-y'''(x)\right )=y''(x) y'''(x)\)

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

Solution method TO DO

Maple
Mathematica

ODE 2304

\(3 y''(x) y''''(x)=5 \left (y'''(x)\right )^2\)

[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]

Solution method TO DO

Maple
Mathematica

ODE 2305

\(-4 y'(x) \left (y'''(x)\right )^2+3 y'(x) y''(x) y''''(x)-3 y''(x)^3=0\)

[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2306

\(-45 y''(x) y'''(x) y''''(x)+9 y''(x)^2 y'''''(x)+40 \left (y'''(x)\right )^3=0\)

[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]

Solution method TO DO

Maple
Mathematica

ODE 2307

\(y^{(n)}(x)=f(x)\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2308

\(y^{(n)}(x)=f\left (y^{(n-2)}(x)\right )\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2309

\(y^{(n)}(x)=f\left (y^{(n-1)}(x)\right )\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2310

\(y^{(n-2)}(x) y^{(n)}(x)=y^{(n-1)}(x)^2\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2311

\(f\left (x,y^{(n)}(x)\right )=0\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2312

\(f\left (x,y^{(n-1)}(x),y^{(n)}(x)\right )=0\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica

ODE 2313

\(f\left (y^{(n-2)}(x),y^{(n-1)}(x),y^{(n)}(x)\right )=0\)

(ODEtools/info) missing specification of intermediate function

Solution method TO DO

Maple
Mathematica