​ The solution of the DE dy/dx + y log y cot x = 0 is A. cos x log y = C B. sin x log y = C ​

Question

The solution of the DE \(\frac{dy}{dx}\) + y log y cot x = 0 is

A. cos x log y = C

B. sin x log y = C

C. log y = C sin x

D. none of these

Answer 1

On differentiating we get

\(\frac{1}{y}\) dy = dt

\( \frac{dt}{t}\) = - cot x dx

log t = -log (sin x) + C

log t + log(sin x) = C

log(tsin x) = C

tsin x = C

(log y)(sin x) = C

Conclusion: Therefore, (log y)(sin x) = C is the solution of \(\frac{dy}{dx}\) + y log y cot x = 0