2020 VJC Promo Q1
It is given that $\frac{\text{d}y}{\text{d}x}+xy={{\text{e}}^{-x}}$ and $y=1$ when $x=0$.
(i)
Find the Maclaurin series for $y$, up to and including the term in ${{x}^{3}}$.
[5]
(ii)
Hence, or otherwise, state the first three non-zero terms of the Maclaurin series for $\frac{\text{d}y}{\text{d}x}$.
[1]
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