Differential EquationHard
Question
A curve passes through the point 
& its slope at any point is given by 
- cos2 
. Then the curve has the equation -
& its slope at any point is given by - cos2 . Then the curve has the equation -Options
A.y = x tan-1 
B.y = x tan-1(1n + 2)
C.y = 
tan-1
tan-1D.none
Solution
- cos2 
Put y = vx then
= v + x 
v + x
= v - cos2v⇒
⇒ tan v = - ln x + c ⇒ tan
= - ln x + cAs it passes through the point (1,
)so c = 1
tan
= -ln x + 1 ⇒ tan 
= ln 
∴ y = x tan-1 (ln
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