Question

The general solution of the differential equation $\frac{dy}{dx}=\frac{1+cos2y}{1-cos2x}$ is

• A. tany-cotx = c (c is a constant).
• B. tan x - cot y = c (c is a constant)
• C. tan y +cot x = c (c is a constant)
• D. tan x + cot y = c (c is a constant)

Answer 1

The correct option is C tan y +cot x = c (c is a constant)

$\frac{dy}{dx}=\frac{1+cos2y}{1-cos2x}$

$\frac{dy}{dx}=\frac{2co{s}^{2}y}{2si{n}^{2}x}$

$se{c}^{2}ydy=cose{c}^{2}xdx$

integrating both sides,

tan y = -cot x + C

tan y + cot x = C