Duffing ODEs - Maple Help

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Duffing ODEs

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, and ?odeadvisor,<TYPE> where <TYPE> is one of: 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; for other differential orders see odeadvisor,types.


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