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Question

The integrating factor of the differential equation dydx=y tan xy2 sec x is

[MP PET 1995; Pb. CET 2002]


A

tanx

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B

secx

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C

-secx

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D

cotx

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Solution

The correct option is B

secx


The differential equation
is dydxy tan x=y2 sec xI.F.=e tan x dx
This is Bernoulli's equation i.e. reducible to
linear equation.
Dividing the equation by y2, we get
1y2dydx1y tan x=sec x............(i)
Put 1y=y1y2dydx=dYdx
Equation (i) reduces to dydx=y tan x=sec xdYdx+Y tan x=sec x, Which is a linear equation
Hence I.F.=e tan x dx=sec x.


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