Consider the following four first-order differential equations.
(1) Indicate whether the equation can be rewritten so that all terms involving y (including dy) are on one side of the equal sign and all terms involving x (including dx) are on the other. Clearly state "Yes" or "No" for each of the four equations.
(2) For every equation you labeled "Yes" in part (a), show one line of algebra that accomplishes the separation of variables. Your work should result in an equation of the form M(y)dy=N(x)dx.
(3) For every equation you labeled "No" in part (a), justify your conclusion with a brief but precise explanation that refers to specific algebraic features of the equation.