Differential equation: Euler's method problem

Hi everyone. I'm having trouble with this problem:

Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem y' = xy - x^{2}, y(0) = 1.

I did this, but I don't know if it's right. I don't even know if I understand the question. :( Here's what I have:

y' = xy - x^{2} = x(y-x)

= 1 + .2(0(1-0)) = 1

So, y(1) = 1.

Am I anywhere close? Thanks for your help. :)

Re: Differential equation: Euler's method problem

Looks OK but I'd say $\displaystyle y(0.2) \approx 1$ (Nod)

If you want to understand better this MIT Math Lecture: Differential Equations - 02 - Euler's Method for y'=f(x,y) might help.

Re: Differential equation: Euler's method problem

What you have calculated (so far) is the Euler approximation to $\displaystyle y(0.2),$ you've gone just one step.

You now have to move on successively to approximations for $\displaystyle y(0.4), y(0.6), y(0.8),$ and finally $\displaystyle y(1).$