The general solution of the differential equation \(\displaystyle\frac{dy}{dx} = \sec^2 x\,\cos^2 y\) is (C is an arbitrary constant)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\tan y = \tan x + C\)
The equation is variables separable. Dividing by \(\cos^2 y\):
\( \displaystyle \frac{dy}{\cos^2 y} = \sec^2 x\,dx \)
\(\sec^2 y\,dy = \sec^2 x\,dx\)
Integrating both sides, with \(\int \sec^2 t\,dt = \tan t\):
\(\tan y = \tan x + C\)