Solve the differential equation.
-$y ^ { \prime } + y \tan x = \cos x , - \pi / 2

Question

Solve the differential equation.
-$y ^ { \prime } + y \tan x = \cos x , - \pi / 2 < x < \pi / 2$
A) $y = x \sin x + C \sin x , - \pi / 2 < x < \pi / 2$
B) $y = x \cos x + C \cos x , - \pi / 2 < x < \pi / 2$
C) $y = x \sin x + C \cos x , - \pi / 2 < x < \pi / 2$
D) $y = x \cos x + C \sin x , - \pi / 2 < x < \pi / 2$

Quizplus · Accepted Answer

The differential equation is a first-order linear equation. The integrating factor is $ \sec x $, and solving it gives $ y = x \cos x + C \cos x $.

Solve the Differential Equation y′+ytan⁡x=cos⁡x,−π/2<x<π/2y ^ { \prime } + y \tan x = \cos x , - \pi / 2 < x < \pi / 2y′+ytanx=cosx,−π/2<x<π/2

Solve the Differential Equation $y ^ { \prime } + y \tan x = \cos x , - \pi / 2 < x < \pi / 2$