Question

Solution of the differential equation $\frac{dy}{dx}+y\sec x=\tan x(\le x<\frac{\pi }{2})$ is

• A. $y(\sec x-\tan x)=(\sec x+\tan x)-x+C$
• B. $y(\sec x+\tan x)=(\sec x-\tan x)-x+C$
• C. $y(\sec x+\tan x)=(\sec x+\tan x)-x+C$
• D. $noneofthese$

Answer 1

Answer: (C)

$y(\sec x+\tan x)=(\sec x+\tan x)-x+C$

$\frac{dy}{dx}+y\sec x=\tan x$

$\frac{dy}{dx}+Py=Q$

If $=\int Pdx=e^{\log |\sec x+\tan x|}$

$=\sec x+\tan x$

$Y\left(IF\right)=\int (Q\times IF)dx+C$

$Y(\sec x+\tan x)=\int \tan x(\sec x+\tan x)+C$

$Y(\sec x+\tan x)=\int \tan x\sec x+\int {\tan }^{2}xdx$

$Y(\sec x+\tan x)=\sec x+\int {\sec }^2-1dx+C$

$Y(\sec x+\tan x)=\sec x+\tan x-x+C$