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

  • question_answer
    The number of solutions of  \[{y}'=\frac{y+1}{x-1},\,y(1)=2\] is [MP PET 2000]

    A)                 None     

    B)                 One

    C)                 Two       

    D)                 Infinite

    Correct Answer: A

    Solution :

                       \[\frac{dy}{dx}=\frac{y+1}{x-1}\] Þ \[\frac{dy}{y+1}=\frac{dx}{x-1}\]         Integrating both sides, \[\int{\frac{dy}{y+1}=\int{\frac{dx}{x-1}}}\]         Þ \[\log (y+1)=\log (x-1)+\log c\]Þ \[(y+1)=(x-1)c\]         At \[x=1\] Þ \[y=-1\] where as \[y(1)=2\]                 Hence, the solution is not possible.


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