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

  • question_answer
    Integral curve satisfying  \[y'=\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}},\ y(1)=2\] has the slope at the point (1, 0) of the curve, equal to       [MP PET 2000]

    A)                 ? 5/3      

    B)                 ? 1

    C)                 1             

    D)                 5/3

    Correct Answer: C

    Solution :

                       \[\frac{dy}{dx}=\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}}\] and \[\frac{dy}{dx}\] is the slope of the curve,                 \ \[{{\left( \frac{dy}{dx} \right)}_{(1,\,0)}}=\frac{1+0}{1-0}=1\].


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