The ConjugateEquation(extremals, parms, parm_values, t, t0) command computes an algebraic equation. Its roots are the conjugate points.

The extremals option can be specified as a list, for example, [a*sin(t) + b*cos(t), c*sinh(t/c)+d*cosh(t/d)].

The extremals option can also be expressed algebraically, for example, A*cosh((t-a)/A).

If there are $n$ extremals, there must be $2n$ parameters.

The parm_values options specifies the list of values of the parameters parms at the extremal points matching the boundary conditions of the problem.

The t0 option is an end point for the independent variable, for example, the left one.

To find any conjugate points, set the returned equation to 0 (zero) and solve.

$\mathrm{with}\left(\mathrm{VariationalCalculus}\right)$

$\left[\mathrm{ConjugateEquation}\,\mathrm{Convex}\,\mathrm{EulerLagrange}\,\mathrm{Jacobi}\,\mathrm{Weierstrass}\right]$

$\mathrm{ConjugateEquation}\left(A\sin \left(t\right)+B\cos \left(t\right)\,\left[A\,B\right]\,\left[1\,0\right]\,t\,0\right)$

$\sin \left(t\right)$