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JEE Main & Advanced Mathematics Differential Equations Question Bank Variable Separable type differential equations

  • question_answer
    Solution of the equation \[\cos x\cos y\frac{dy}{dx}=-\sin x\sin y\]is [DSSE 1987]

    A)                 \[\sin y+\cos x=c\]

    B)                 \[\sin y-\cos x=c\]

    C)                 \[\sin y.\cos x=c\]  

    D)                 \[\sin y=c\cos x\]

    Correct Answer: D

    Solution :

                       \[\cos x\cos y\frac{dy}{dx}=-\sin x\sin y\]                    Þ \[\frac{\cos y}{\sin y}dy=-\frac{\sin x}{\cos x}dx\] Þ \[\cot ydy=-\tan xdx\]                    On integrating, we get                                 \[\log \sin y=\log \cos x+\log c\]Þ\[\sin y=c\cos x\].


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