2022 EJC Promo Q2
It is given that $y={{\text{e}}^{2x}}\cos x$.
(a)
Show that $\frac{{{\text{d}}^{2}}y}{\text{d}{{x}^{2}}}=4\frac{\text{d}y}{\text{d}x}-5y$.
[3]
(b)
Find the Maclaurin series for $y$ up to the term in ${{x}^{2}}$.
[2]
(c)
Hence, show that the Maclaurin series for ${{\text{e}}^{x}}\sqrt{\cos x}$ is $1+x+\frac{1}{4}{{x}^{2}}$, up to the term in ${{x}^{2}}$.
-[2]
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