Original unknown functions are expressed by introducing auxiliary unknown functions and integral relations of auxiliary unknown functions. The dual integral equations are decoupled and reduced to Abel integral equations by using Sonine first finite integral formula and the it is further reduced to regularized Fredholm singular integral equations with logarithmic kernels of first kind by Abel anti-transformation. Thus general solutions of singular integral equations are given. And then analytic solutions of dual integral equa- tions are obtained. Simultaneously the equivalence between dual integral equations and corresponding Fredholm singular integral equations with logarithmic kernel of first kind, the existence and uniqueness of solutions are proved exactly.