Final answer:
The equation 2xy2y′ = 2x²y − 5x³ is a separable equation because it can be rearranged to separate variables y and x on different sides of the equation, and it is not linear, Bernoulli, or homogeneous.
Step-by-step explanation:
The equation provided, 2xy2y′ = 2x²y − 5x³, is not a linear equation, because it does not have the form y = a + bx, where a is the y-intercept and b is the slope. This equation can be considered a separable equation because it can be rewritten in the form of a differential equation that allows the variables y and x to be separated on different sides of the equation. Furthermore, this equation does not match the criteria of a Bernoulli equation, as it does not have the form y' + p(x)y = q(x)y^n, and it is not a homogeneous equation either since it includes terms that do not have the same degree when combined. Therefore, the correct answer is (b) a separable equation.