Science:Math Exam Resources/Courses/MATH215/December 2013/Question 07 (c)/Statement

Consider the following initial value problem for a first-order autonomous ODE:

${\frac {dy}{dt}}=-y(y-1)^{2},\quad y(0)=y_{0}$

(c) Again if $y_{0}=3/2$, use Euler’s method with the larger step size $h=2$ to approximate the solution $y(2)$ at time $t=2$. Predict what will happen if you continue to use this scheme (with $h=2$) to approximate $y(t)$ for large $t$. Compare this with your result from part (a), and explain any discrepancies.