What is the solution of the differential equation \( \cos\left(\frac{dy}{dx}\right) = p \) when \( y(0) = q \) ?
- A. \cos\left(\frac{y-q}{x}\right) = p ✓
- B. \cos\left(\frac{y-p}{x}\right) = q
- C. \cos^{-1}\left(\frac{y-q}{x}\right) = p
- D. \cos^{-1}\left(\frac{y-p}{x}\right) = q
Correct Answer: A. \cos\left(\frac{y-q}{x}\right) = p
Explanation
Taking the inverse cosine gives \( \frac{dy}{dx} = \cos^{-1} p \). Integrating yields \( y = x \cos^{-1} p + C \). Applying the initial condition \( y(0)=q \) gives \( C=q \), leading to the solution.
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