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We are given the differential equation: $$ \frac{dy}{dx} + y = e^{-x} $$ with initial condition: $$ y(0) = 2 $$ and step size $h = 0.5$ --- ### Step 1: Rearranging the differential equation We need to express $\frac{dy}{dx}$ explicitly: $$ \frac{dy}{dx} = e^{-x} - y $$ This is now in the form suitable for Euler’s method: $$ y_{n+1} = y_n + h \cdot f(x_n, y_n) $$ ___ _______ ________ ____ __________ ______ ______ ____ _____.
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