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JEE Main & Advanced Mathematics Differential Equations Question Bank Application of differnetial equations

  • question_answer
    The equation of a curve passing through \[\left( 2,\frac{7}{2} \right)\] and having gradient \[1-\frac{1}{{{x}^{2}}}\]at\[(x,\,y)\]is

    A)                 \[y={{x}^{2}}+x+1\]      

    B)                 \[xy={{x}^{2}}+x+1\]

    C)                 \[xy=x+1\]           

    D)                 None of these

    Correct Answer: B

    Solution :

                       We have \[\frac{dy}{dx}=1-\frac{1}{{{x}^{2}}}\] Þ \[y=x+\frac{1}{x}+c\]         This passes through \[\left( 2,\frac{7}{2} \right)\], \ \[\frac{7}{2}=2+\frac{1}{2}+c\] Þ \[c=1\]                 Thus the equation of the curve is \[y=x+\frac{1}{x}+1\] or\[xy={{x}^{2}}+x+1\].


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