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Question

If y=2πx-1cosecx is the solution of the differential equation, dydx+pxy=2πcosecx;0<x<π2, then the function px is equal to


A

cosecx

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B

cotx

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C

tanx

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D

secx

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Solution

The correct option is B

cotx


Explanation for the correct option.

Step 1. Find the differential equation.

Differentiate the equation y=2πx-1cosecx with respect to x.

dydx=ddx2πx-1cosecxdydx=2πcosecx+2πx-1(-cosecxcotx)dydx=2πcosecx-2πx-1cosecxcotxdydx=2πcosecx-ycotxy=(2πx-1)cosec(x)dydx+ycotx=2πcosecx

Step 2. Find the function px.

Comparing the given differential equation dydx+pxy=2πcosecx, with the equation found dydx+ycotx=2πcosecx it can be seen that the function p(x) corresponds to cotx.

So the function p(x) is equal to cotx.

Hence, the correct option is B.


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