Trigonometric EquationHard
Question
Solution of the differential equation cos x dy = y(sin x - y) dx, 0 < x < 
is
isOptions
A.y sec x = tan x + c
B.y tan x = sec x + c
C.tan x = (sec x + c)y
D.sec x = (tan x + c)y
Solution
cos x dy = y(sin x - y) dx
= y tanx - y2 sec x
tan x = - sec x
Let
-
- t tan x = - sec x ⇒ + (tan x) t = sec x.
I.F. = e∫ tan x dx = sec x
Solution is t(I.F) = ∫ (I.F) sec x dx
sec x = tan x + c
= y tanx - y2 sec x tan x = - sec xLet
-
- t tan x = - sec x ⇒ + (tan x) t = sec x.I.F. = e∫ tan x dx = sec x
Solution is t(I.F) = ∫ (I.F) sec x dx
sec x = tan x + cCreate a free account to view solution
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