A Note on ODEs from Mirror Symmetry
  We give close formulas for the counting functions of rational curves on complete intersection Calabi-Yau manifolds in terms of special solutions of generalized hypergeometric differential systems. For the one modulus cases we derive a differential equation for the Mirror map, which can be viewed as a generalization of the Schwarzian equation. We also derive a nonlinear seventh order differential equation which directly governs the instanton corrected Yukawa coupling. 
A. Klemm, B.H. Lian, S.S. Roan and S.-T. Yau