Differential EquationHard
Question
The differential equation 
+ y + cot2 x = 0 must be satisfied by
+ y + cot2 x = 0 must be satisfied byOptions
A.y = 2 + c1 cos x + 
sin x
sin xB.y = cos x . ln 
+ 2
+ 2C.y = 2 + c1 cos x + c2 sin x + cos x log 
D.all the above
Solution
(A)
= - c1 sin x + 
cos x
= - c1 cos x - 
sin x = 2 - y
+ y + 2 = 0
(B)
= cos x 
- sin x ln 
= cot x - sin x ln 
= - cosec2 x - 
= - cot2 x - 2 - cos x ln 
+ y + cot2 x = 0
(C)
= - c1 sin x + c2 cos x + 
= - (c1 cos x + c2 sin x) + 
= - c1 cos x - c2 sin x - cot2 x - 2 - cos x ln 
+ y + cot2 x = 0
= - c1 sin x + cos x = - c1 cos x - sin x = 2 - y + y + 2 = 0(B)
= cos x - sin x ln = cot x - sin x ln = - cosec2 x - = - cot2 x - 2 - cos x ln + y + cot2 x = 0(C)
= - c1 sin x + c2 cos x + = - (c1 cos x + c2 sin x) + = - c1 cos x - c2 sin x - cot2 x - 2 - cos x ln + y + cot2 x = 0Create a free account to view solution
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