To approximate the solution of dxdy=x2−y with y(0)=0.5, a student proceeds from x=0 to x=0.25 in three stages:
• first increment Δx=0.10 (from 0 to 0.10)
• second increment Δx=0.10 (to 0.20)
• third increment Δx=0.05 (to 0.25)
Each time the student updates y using the derivative evaluated at the left end of the subinterval.
What value does the student obtain for y(0.25)?
a) 0.392
b) 0.406
c) 0.388
d) 0.369