Let the arithmetic function φ(n) be Euler function, and let the arithmetic function φe(n) be generalized Euler function. Based on the solvability of the Diophantine equation mixed with the Euler function φ(n) and the generalized Euler functionφe(n), the issue of solving the integer solutions of the equation φ(ab)=11φ2(a)+13φ2(b) was proposed. By using the properties of the functionsφ(n) andφ2(n), and combination of classification and segmentation, the 21 positive integer solutions of the equation were obtained.