I am trying to understand an example in my book and something isn't making sense to me. The problem is: Use the improved Euler method to calculate approximate values of the solution of the initial value problem .

I have found that . Assuming that h=.025 we then get .

It is after this where I'm getting confused. The equation in my book is . Using this we get .

I cannot for the life of me figure out where the 0.5 is coming from. Can someone show me where it's coming from?