Integration of differential equations by ${\mathcal{C}}^{\mathrm{\infty }}$-structures

Several integrability problems of differential equations are addressed by using the concept of ${\mathcal{C}}^{\mathrm{\infty }}$-structure, a recent generalization of the notion of solvable structure. Specifically, the integration procedure associated with ${\mathcal{C}}^{\mathrm{\infty }}$-structures is used to integrate to a Lotka-Volterra model and several differential equations that lack sufficient Lie point symmetries and cannot be solved using conventional methods.