Question
If 
, then 
is
- 1
- p
- 0
- –p
Hint:
In this question, given is, ycosx + xcosy =π , we have to find the value of y’’ (0). Firstly, separate the y and find it second derivate with respect to x.
The correct answer is: 0
Here we have to find the value of y’’ (0).
Firstly, we have given,
y cosx + x cosy = π ... (1)
Differentiating (1) w.r.t x
−y sinx + y′cosx + cosy − (x siny)y′ = 0
Or
−y sinx + cosy + y′(cosx−xsiny) =0 ... (2)
Again differentiate (2) w.r.t. x for second derivative,
−y cosx − y′ sinx − (−siny ) y′ + y′′ [ cosx – xsiny ] + y′ (−sinx − 1. siny − xcosy.y′) = 0 ... (3)
Putting x=0 in (1), we get, y = π
Putting x=0 and y = π in (2),
we get, 0 + cosπ + y′ ( −1 −π sinπ)
or
−1−y′ = 0
∴y′ = −1
Putting x=0 and y= π and y′=1 in (3), we get,
y′0) =0.
Therefore, the correct answer is 0.
In this question, we have given ycosx + xcosy =π . Differentiate this equation with request to x and do separate second derivate and find the value of it.
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is
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when 
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is
is
