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JCECE Engineering JCECE Engineering Solved Paper-2012

  • question_answer
    The function defined by the equation \[xy-\log y=1\]satisfies\[x(yy''+y{{'}^{2}})-y''+kyy'=0\]. Find the value of\[k\].

    A) \[-3\]                    

    B) \[3\]

    C) \[1\]                                     

    D) \[-1\]

    Correct Answer: B

    Solution :

    Given, equation is                 \[xy-\log y=1\] On differentiating it w.r.t\[.x,\] we get                 \[xy'+y\cdot 1-\frac{1}{y}\cdot y'=0\] \[\Rightarrow \]               \[xyy'+{{y}^{2}}-y'=0\] Again, differentiating w.r.t. x, we get                 \[(xy-1)y''+y'(xy'+y\cdot 1)+2yy'=0\] \[\Rightarrow \]               \[x(yy''+y{{'}^{2}})-y''+3yy'=0\] Comparing it with the given equation, we get                 \[k=3\]


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