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Duffing ODEs
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Description
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The general form of the Duffing ODE is given by:
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Duffing_ode := diff(y(x),x,x)+y(x)+epsilon*y(x)^3 = 0;
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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:
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Examples
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![[odeadvisor]](/support/helpjp/helpview.aspx?si=7233/file04350/math28.png)
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![[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]]](/support/helpjp/helpview.aspx?si=7233/file04350/math35.png)
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See Also
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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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