General solution of the differential equation x(1+ y)dx- y ,(1+ x)dy=0 is

MHT CET 2023 Mathematics question

General solution of the differential equation is

(A), where c is a constant of integration
(B), where c is a constant of integration
(C), where c is a constant of integrationCorrect
(D), where c is a constant of integration

Answer: (C)

Solution

Separate the variables: \cos x(1+\cos y)\,dx=\sin y(1+\sin x)\,dy\Rightarrow\frac{\cos x}{1+\sin x}dx=\frac{\sin y}{1+\cos y}dy. Integrate: (since ). So $|(1+

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Question ID VK-098358