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Bessel and Modified Bessel ODEs
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Description
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The general form of the Bessel ODE is given by the following:
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Bessel_ode := x^2*diff(y(x),x,x)+x*diff(y(x),x)+(x^2-n^2)*y(x);
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| (1) |
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The general form of the modified Bessel ODE is given by the following:
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modified_Bessel_ode := x^2*diff(y(x),x,x)+x*diff(y(x),x)-(x^2+n^2)*y(x);
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| (2) |
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where n is an integer. See Abramowitz and Stegun - `Handbook of Mathematical Functions`, section 9.6.1. The solutions for these ODEs are expressed using the Bessel functions in the following examples.
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Examples
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![[odeadvisor]](/support/helpjp/helpview.aspx?si=7229/file04347/math45.png)
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![[_Bessel]](/support/helpjp/helpview.aspx?si=7229/file04347/math52.png)
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![[[_Bessel, _modified]]](/support/helpjp/helpview.aspx?si=7229/file04347/math59.png)
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The Bessel ODEs can be solved for in terms of Bessel functions:
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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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