Differential Equations Question 347
Question: Solution of the differential equation $ \frac{dy}{dx}+y{{\sec }^{2}}x=\tan x{{\sec }^{2}}x $ is
[DCE 2001, 05]
Options:
A) $ y=\tan x-1+c{e^{-\tan x}} $
B) $ y^{2}=\tan x-1+c{e^{\tan x}} $
C) $ y{e^{\tan x}}=\tan x-1+c $
D) $ y{e^{-\tan x}}=\tan x-1+c $
Show Answer
Answer:
Correct Answer: A
Solution:
I.F. = $ {e^{\int{{{\sec }^{2}}xdx}}}={e^{\tan x}} $
\ Solution is $ y{e^{\tan x}}=c+\int{\tan x{e^{\tan x}}{{\sec }^{2}}xdx} $
Therefore $ y=c{e^{-\tan x}}+\tan x-1 $ .
BETA
