not to sure how to do this question, thanks for any help
Euler, without correction, is the simplest possible method of solution approximation. Are you SURE you are serious about this class? Really, if you are struggling with this, you will not be a happy camper at all in the real near future.
Just step through it.
dy/dx = 1 + xy
y(1) = 0
Then dy/dx around (1,0) is approximately 1 + (1)(0) = 1
y(1.1) = 0 + 0.1*1 = 0.1
The dy/dx around (1.1,0.1) = 1 + 1.1*0.1 = 1 + 0.11 = 1.11
y(1.2) = 0.1 + 0.1*1.11 = 0.211
The dy/dx around (1.2,0.211) = 1 + 1.2*0.211 = 1 + 0.12532 = 1.12532
Two things questionable with this presentation:
1) It was not necessary to calculate the last value. We were interested in y(1.2).
2) I carried all decimal places in all calculations. One may wish to concern oneself with proper significant figures. However, it pays to pay attention to all kinds of error.