Question

General solution of the differential equation $\frac{dy}{dx}+y\tan x=\sec x$ is
(Where $C$ denotes constant of integration)

• A. $y\sec x=\tan x+C$
• B. $y\tan x=\sec x+C$
• C. $\tan x=y\tan x+C$
• D. $x\sec x=\tan y+C$

Answer 1

Answer: (A)

$\text{ I.F. }=e^{\int \tan xdx}=e^{\ln \sec x}=\sec x$
$y\sec x=\int {\sec }^{2}xdx$
$=\tan x+C$
$y\sec x=\tan x+\text{ C. }$