Mathematics

Euler's method builds an approximate solution by taking small steps along the slope at each point. Starting from your known point $(0,1)$, you'll use the differential equation $\frac{dy}{dx}=x+y$ to find the slope, then move horizontally by $0.5$ and vertically by (slope) $\times 0.5$. Repeat this process twice to reach $x=1$, tracking how $y$ changes at each step.

Euler's method builds an approximate solution by taking small steps along the slope at each point. Starting from your known point $(0,1)$, you'll use the differential equation $\frac{dy}{dx}=x+y$ to find the slope, then move horizontally by $0.5$ and vertically by (slope) $\times 0.5$. Repeat this process twice to reach $x=1$, tracking how $y$ changes at each step.