When solving the common form of the special Ricatti
$$y' = q(x) + p(x)y + r(x)y^2$$
The first step is to assume a solution of:
$$y(x) = y_1(x) + z(x)$$ Which reduces the Differential Equation into a Bernoulli Equation:
$$z(x)' = p(x)z(x) +r(x)[2y_1(x) z(x) + z(x)^2]$$
However, doesn't this imply that the differential eqution has two linearly independant solutions? Shouldn't a Differential Equation of order one contain only one solution?