Duffing ODEs - Maple Help

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Duffing ODEs

 

Description

Examples

Description

• 

The general form of the Duffing ODE is given by:

Duffing_ode := diff(y(x),x,x)+y(x)+epsilon*y(x)^3 = 0;

Duffing_ode:=ⅆ2ⅆx2yx+yx+εyx3=0

(1)
  

See Bender and Orszag, "Advanced Mathematical Models for Scientists and Engineers", p. 547. The solution of this type of ODE can be expressed in terms of elliptic integrals, as follows:

Examples

withDEtools,odeadvisor

odeadvisor

(2)

odeadvisorDuffing_ode

_2nd_order,_missing_x,_Duffing,_2nd_order,_reducible,_mu_x_y1

(3)

dsolveDuffing_ode

yx=_C2JacobiSN122ε+4x+_C12_C22εε2,_C2ε+2εε+22_C22εε2

(4)

See Also

DEtools

odeadvisor

dsolve

quadrature

missing

reducible

linear_ODEs

exact_linear

exact_nonlinear

sym_Fx

linear_sym

Bessel

Painleve

Halm

Gegenbauer

Duffing

ellipsoidal

elliptic

erf

Emden

Jacobi

Hermite

Lagerstrom

Laguerre

Liouville

Lienard

Van_der_Pol

Titchmarsh

odeadvisor,types

 


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