Find a particular solution satisfying the given condition: $\cos \left(\frac{dy}{dx}\right) = a$ $(a \in R)$; $y = 1$ when $x = 0$.
- A$y = x \cos^{-1}(a) + 1$
- B$y = x \cos(a) + 1$
- C$y = x \sin^{-1}(a) + 1$
- D$y = x \cos^{-1}(a) - 1$
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