I am trying to use the Improved Euler's Method to solve a homework problem, but I am having trouble with the notation and my book is extremely unhelpful.

Where the lower formula is the Improved Euler's method.

I am given:

y = 5e^(x(x+2))

y' = 2y(x+1)

y(0) = 5

dx = .3 (I'm guessing this is step size...)

My main difficulty is notation and conception of the problem: the notation is confusing me, and I'm not sure what is actually happening in the formula. Does f(x,y) mean the function with x and y substituted, or something else? The problem asks for the first approximation. If someone could explain the problem in steps that would be great.