In contrast to the standard approach in energy economics, this paper assumes that physical capital accumulation is relatively more energy-intensive than consumption. By means of Gaussian hypergeometric functions, we provide a closed-form representation of the optimal solution paths of our variables in levels, whatever the initial conditions (i.e., global dynamics). We find that, in general, the optimal trajectories are non-monotonic. P.S. Dasgupta and G.M. Heal [Review of Economic Studies (special number), 3-28 (1974)] pointed out this result (local dynamics) for the optimal consumption in a model with identical technology for both physical capital accumulation and consumption. However, our paper introduces five novelties with respect to their study, namely, global dynamics, the importance of the proportion of non-renewable energy resources to endowment of physical capital [S(0)/K(0)], the role of technical progress, U-shaped behaviour of consumption, and non-monotonicity of resource extraction.