Math Help - Differential equation: Euler's method problem

1. 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 - x2, 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 - x2 = x(y-x)
= 1 + .2(0(1-0)) = 1
So, y(1) = 1.

Am I anywhere close? Thanks for your help.

2. Re: Differential equation: Euler's method problem

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

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

3. Re: Differential equation: Euler's method problem

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

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