Let the solution curve x = x(y), 
, of the differential equation (log e (cos y)) 2 cosy dx - (1 + 3x log e (cos y))siny dy = 0 satisfy 
. If 
, where m and n are coprime, then ran is equal to
Text Solution
Verified by Experts12
(12)
Given,
(log e (cos y)) 2 cos y dx -(1 + 3x log e (cos y))sin y dy = 0
Which is a linear differential equation,
So, Integrating factor will be, IF 
So, solution of differential equation is given by,
Now using the given value of 
We get, c = 0
Hence, 
Now finding, 
Now on comparing with 
we get, m = 4, n = 3
Hence, mn = 12
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