​ The solution of the x dy/dx = cot y is A. x cos y = C B. x tan y = C ​

Question

The solution of the x \(\frac{dy}{dx} \) = cot y is

A. x cos y = C

B. x tan y = C

C. x sec y = C

D. None of these

Answer 1

x \(\frac{dy}{dx} \) = cot y

Separating the variables, we get,

\(\frac{dy}{coty} = \frac{dx}{x}\)

tan y dy = \(\frac{dx}{x} \)

Integrating both sides, we get,

\(\int\) tan y dy = \(\int\) \(\frac{dx}{x} \)

log sec y = log x + log c

x cos y = c

Hence, A is the correct answer.