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Complete Elliptic Integral ODEs
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Description
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The general forms of the elliptic ODEs are given by the following:
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elliptic_I_ode := diff(x*(1-x^2)*diff(y(x),x),x)-x*y(x)=0;
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elliptic_II_ode := (1-x^2)*diff(x*diff(y(x),x),x)+x*y(x)=0;
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See Gradshteyn and Ryzhik, "Tables of Integrals, Series and Products", p. 907. The solution to this type of ODE can be expressed in terms of the EllipticK and EllipticCK functions.
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Examples
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![[odeadvisor]](/support/helpjp/helpview.aspx?si=7235/file04366/math41.png)
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![[[_elliptic, _class_I]]](/support/helpjp/helpview.aspx?si=7235/file04366/math62.png)
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![[[_elliptic, _class_II]]](/support/helpjp/helpview.aspx?si=7235/file04366/math69.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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