Question

Solution of the differential equation:

dy/dx + y cot x = 2 cosx

Answer 1

\(\frac{dy}{dx} + \frac{y \cos x}{\sin x} = 2 \cos x\)

⇒ \(\sin x \frac{dy}{dx} + y\cos x = \sin 2x\)

⇒ \(y\sin x = \frac{-\cos 2x}2 + c\)

\(y\sin x = - \cos^2 + c_1\)     \([c + 1/2 = c_1]\)

⇒ \(y\sin x + cos^2 x = c_1\)