 For example, in the case formula_8, making the substitution formula_9 in the differential equation formula_10 produces the equation formula_11, which is a linear differential equation.Let formula_12 and
be a solution of the linear differential equation
Then we have that formula_15 is a solution of 
And for every such differential equation, for all formula_17 we have formula_18 as solution for formula_19.Consider the Bernoulli equation 
(in this case, more specifically Riccati's equation).