Improving explicit bounds for the solutions of second order linear differential equations

This paper improves the algorithm for the construction of explicit bounds for the solutions of second order linear differential equations of the type [p(x)y′(x)]′+q(x)y(x)=0[p(x)y′(x)]′+q(x)y(x)=0, p(x),q(x)>0p(x),q(x)>0, x>x0x>x0 described in a recent paper of the authors. The main improvements come from the introduction of new functionals devised by Trevisan and from the application of an enhanced version of the mean value theorem for integrals when some functions of the integrand are monotonic.