Question

The general solution of the differential equation $\frac{dy}{dx} + (\sec x \csc x)y = \cos^2 x$ is

• A. $y \sec^2 x = \sin^2 x + c$
• B. $y \sec^2 x = \tan x + c$
• C. $y \tan x = \sin x \cos x + c$
• D. $2y \tan x = \sin^2 x + c$

Hint:

To solve a linear differential equation $\frac{dy}{dx}+P(x)y=Q(x)$, first calculate the integrating factor $I(x) = e^{\int P(x)dx}$. The general solution is then given by the formula $y \cdot I(x) = \int Q(x) \cdot I(x) dx + C$.

Answer 1

The Correct Option is D