Question

Use Euler’s method with a step size of h = 0.2 to estimate y(1) for the initial-value problem:
dy/dx = x + y , y(0) = 1.

Answer 1

i got y(1) = 0.8 + 0.2(0.8+1.8) = 1.32

Answer 2

the first step will be with starting at y=1and it will increase by the derivative at (0,1)

so the after the first step, x=0+0.2=0.2 and y =1+(0+1)*.2
which gives a y-value of 1.2 so the new point is (0.2,1.2) those are our new x,y

Answer 3

we then use that again, and our next x=0.4, and then the new y= 1.2+ (0.2+1.2)*.2= 1.48

(0.4,1.48) is our second (x,y). now keep going three more times to get the final answer at x=1