Ellipsoidal ODEs - Maple Programming Help

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Ellipsoidal ODEs

Description

 • The general form of the ellipsoidal ODE is given by the following:
 > with(DEtools,odeadvisor);
 $\left[{\mathrm{odeadvisor}}\right]$ (1)
 > ellipsoidal_ode := diff(y(x),x,x) = (a+b*k^2*sin(x)^2+q*k^4*sin(x)^4)*y(x);
 ${\mathrm{ellipsoidal_ode}}{:=}\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{x}}^{{2}}}{}{y}{}\left({x}\right){=}\left({a}{+}{b}{}{{k}}^{{2}}{}{{\mathrm{sin}}{}\left({x}\right)}^{{2}}{+}{q}{}{{k}}^{{4}}{}{{\mathrm{sin}}{}\left({x}\right)}^{{4}}\right){}{y}{}\left({x}\right)$ (2)
 > odeadvisor(ellipsoidal_ode);
 $\left[{\mathrm{_ellipsoidal}}\right]$ (3)
 See Arscott, "The Land Beyond Bessel: A Survey of Higher Special Functions".

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