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Question

The general solution of the differential equation dydx=cotxcoty is


A

cosx=ccosecy

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B

sinx=csecy

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C

sinx=ccosy

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D

cosx=csiny

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Solution

The correct option is B

sinx=csecy


Find the general solution of the differential equation

Given, dydx=cotxcoty

dycoty=cotxdxtanydy=cotxdxlogsecy=logsinx+logctanxdx=logsec(x)+ccotxdx=logsinx+csecy=csinxcsecy=sinxsinx=csecy

Hence, option (B) is the correct answer.


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