A generalization of the confluent hypergeometric differential equation given by y'' + ((2A)/x + 2f' + (b h')/h - h' - h''/h') y' + [((b h')/h - h' - h''/h')(A/x + f') + (A(A - 1))/x^2 + (2A f')/x + f'' + f^(, 2) - (a h^(, 2))/h] y = 0. The solutions are given by y_1 | = | x^(-A) e^(-f(x)) _1 F_1(a;b;h(x)) y_2 | = | x^(-A) e^(-f(x)) U(a, b, h(x)), where _1 F_1(a;b;z) is a confluent hypergeometric function of the first kind and U(a, b, z) is a confluent hypergeometric function of the second kind.