We present two algorithms for computing hypergeometric solutions of second order linear differential operators with rational function coefficients. Our first algorithm searches for solutions of the form(1)exp(∫rdx)⋅2F1(a1,a2;b1;f) where r,f∈Q(x)‾, and a1,a2,b1∈Q. It uses modular reduction and Hensel lifting. Our second algorithm tries to find solutions in the form(2)exp(∫rdx)⋅(r0⋅2F1(a1,a2;b1;f)+r1⋅2F1′(a1,a2;b1;f)) where r0,r1∈Q(x)‾, as follows: It tries to transform the input equation to another equation with solutions of type (1), and then uses the first algorithm.