Using Euler's method with step size $0.5$ and starting point $f(1) = 3$, approximate $f(2)$ for the differential equation $\dfrac{dy}{dx} = 2x$.

Core Concept

From $(1,3)$ with slope $2(1)=2$, one step reaches $(1.5,4)$; from there the slope is $2(1.5)=3$, so the second step reaches $(2,4+0.5\cdot 3) = 5.5$.