Herein the physically and mathematically significant semilinear hyperbolic equation u xt = f(u) , where f(u) is an arbitrary smooth function of u and which encompasses Liouville equation as its particular form has been analysed via the isovector approach. Following the procedure given in [1], the components of isovector fields have been tabulated for nine different forms of f(u). The corresponding orbital equations have been solved only for five physically interesting choices of f(u). The solutions of the orbital equations under certain conditions yield invariant groups of transformation which reduce the given partial differential equation to a non-linear ordinary differential equation (NLODE), which has either been solved exactly or reduced to standard forms. However, for the case when f(u) = e nu , n ≠ = 0 which corresponds to the case of Liouville equation, the Nlode has been solved via Noether's theorem, and it has resulted in a closed form exact solution that doesn't seem to have been reported earlier. Further, two more solutions to Liouville equation have been arrived at via standard techniques.