(a) Solve $\left(D^{2}+2 D+1\right) y=\cos 2 x+x^{3}$.
Explanation
The differential equation is solved by first finding the complementary function and the particular integral. The complementary function is given by $y_{c}=e^{-x} (c_{1} \cos x+c_{2} \sin x)$ and the particular integral is given by $y_{p}=A \cos 2 x+B x^{3}$.
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