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

  • question_answer
    The differential equation \[\cot y\,\,dx=x\,\,dy\] has a solution of the form     [Orissa JEE  2002]

    A)                 \[y=\cos x\]           

    B)                 \[x=c\sec y\]

    C)                 \[x=\sin y\]            

    D)                 \[y=\sin x\]

    Correct Answer: B

    Solution :

                       \[\cot y.dx=x.dy\] Þ \[\frac{dx}{x}=\frac{dy}{\cot y}\] Þ \[\frac{dx}{x}=\tan y.dy\]         Integrating both sides,                                 \[\log x=\log \sec y+\log c\] Þ \[x=c\sec y\].


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