jacobi_equation takes five or six arguments :
The return value contains the Jacobi equation
|fy′ y′(y0,y0′,t) h′||⎞|
If the Jacobi equation has a solution such that h(a)=0, h(c)=0 for some c∈(a,b] and h not identically zero on [a,c], then y0 does not minimize the functional F. It is said that c is conjugate to a. The function y0 minimizes F if fy′ y′(y0,y0′,t)>0 for all t∈[a,b] and there are no points conjugate to a in (a,b].
If the Jacobi equation can be solved by dsolve, a sequence containing the equation (3) and its solution is returned. Otherwise, if (3) cannot be solved immediately, only the Jacobi equation is returned.
For example, input :