MORE DETAILED HOMEWORK4 HINT: I just want to emphasise that part A) and part B) of your homework do NOT involve solving ODE, or much messing around with equations. The skill is drawing graphs of functions, and in the context of Autonomous Equations, relating the graph  to a sketch of the solutions of the equation.

In this context, to graph a function, you just need to find ALL the zeroes of the function, and find out when the function is positive, and when it is negative - you can plug in numbers to check this if you can't understand the equation. The most effective ways to find zeroes of a polynomial is to factorize - that is to write as a product where each term contains no power of y greater than 1.

Example: Find zeroes of f(y) = y^2 + 3y and sketch f(y).   We write f(y) = y^2 +3y = y(y+3), and we can then read off that the zeroes are 0 and -3.

Sketch f(y): When y >0, both y and (y+3) are positive, so f(y) is positive. Between 0 and -3, y is negative, but (y+3) is positive, so f(y) is negative. When y<-3, both y and y-3 are negative, so f(y) is positive. You now have all the info required to sketch f(y).