# Euler's Approximation

1. Sep 14, 2015

### UltimateSomni

1. The problem statement, all variables and given/known data
y'+y=3+x y(0)=1
(a) Find approximate values of the solution of the given initial value problem at t = 0.1, 0.2,
0.3, and 0.4 using the Euler method with h = 0.1.

2. Relevant equations
yn+1 = yn + f(x0, y0)(x-x0). Adjusting 0 for the next number as we go up

3. The attempt at a solution
I'm not looking to have the whole thing solved I'm just looking to solve the very first one and if I figure it out I can go from there.
So I solved for y which gets me
y= -e^-x +x +2. I checked this solution on wolfram alpha.
y1=y0 + (-e^-x +x +2)*h= 1 +(-1+0+2)*.1=1.1. According the textbook its 1.2. It feels so close.

2. Sep 14, 2015

### RUber

I think you solved the Diff Eq. and the question asked you to apply the method.
Start with y' = 3+ x - y. I am confused by your mixing of t and x. I will assume that they are supposed to be the same variable.
y(0) = 1, x0 = 0.
Then y(.1) ~ y(0) + (3+x0 -y0)(.1) = 1 + (3-1)*.1 = 1.2.
Next, use y(.1) and x(.1) in the formula to iterate to the approximation for y(.2). And on and on.

3. Sep 14, 2015

### UltimateSomni

Yup, I knew whatever error I made it had to be as obvious as possible. Thank you so much.