The general form of Bernoulli's equation is given by:

Bernoulli_ode := diff(y(x),x)+f(x)*y(x)+g(x)*y(x)^a;

where f(x) and g(x) are arbitrary functions, and a is a symbolic power. See Differentialgleichungen, by E. Kamke, p. 19. Basically, the method consists of making a change of variables, leading to a linear equation which can be solved in general manner. The transformation is given by the following: