# Math Help - Improved Euler's Method Help

1. ## Improved Euler's Method Help

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.

2. Usually they tell you that $y'=f(x,y)$.

So in your case $f(x,y)=2y(x+1)$ and $y_0=y(x_0)=5$ and $x_0 = 0$.

So find $z_1$ and then $y_1, x_1$, then $z_2, y_2, x_2$, etc.

They should probably mention that $x_n = x_{n-1}+\Delta x$

(Usually $h$ is used for the step size though.)