Let $f$ satisfy $\dfrac{dy}{dx} = y - 1$ with $f(0) = 2$. Using Euler's method with two steps of size $0.5$, approximate $f(1)$.

Core Concept

At $(0,2)$ the slope is $1$, so the first step gives $2 + 0.5 = 2.5$; at $(0.5,2.5)$ the slope is $1.5$, so the second step gives $2.5 + 0.5(1.5) = 3.25$.