Final answer:
The coefficient functions for the given differential equation are M(x,y) = x^2 + 4y^2 and N(x,y) = 3xy. By substituting y=ux to make the equation separable, it involves terms with dx and du, but further steps are required to find the exact separable form.
Step-by-step explanation:
The student's question is about solving the differential equation (x2+4y2)dx/dy=3xy. First, we should identify the coefficient functions M(x,y) and N(x,y) which are presented in the equation. The coefficient function M(x,y) is x2 + 4y2 and N(x,y) is 3xy, as they are the terms included in the equation in front of dx/dy and y, respectively.
For part (b), using the substitution of y=ux, we can rewrite the equation to be separable. This results in an equation of the form involving dx and du. However, since the question does not provide the exact form of the separable equation after the substitution, we can't provide the precise terms without further steps which include differentiating y=ux with respect to x and then substituting back into the original equation to separate the variables.