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\(\frac{a}{b}\)
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Consider the differential equation \(\dfrac{dy}{dx} = x+y\) with the initial condition \(y(0)=1\).
Find the first three non-zero terms of the Maclaurin series for \(y(x)\).
Hence, find an approximate value for \(y(0.2)\).
Solve the differential equation to find the particular solution for \(y(x)\).
Find the percentage error in your approximation from part (b), correct to 3 significant figures.
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