2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Differential Equations

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

  • question_answer
    The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes though the point (4, 3). The equation of the curve is

    A)                 \[{{x}^{2}}=y+5\]           

    B)                 \[{{y}^{2}}=x-5\]

    C)                 \[{{y}^{2}}=x+5\]           

    D)                 \[{{x}^{2}}=y-5\]

    Correct Answer: C

    Solution :

                       Accordingly \[\frac{dy}{dx}=\frac{1}{2y}\]Þ\[2ydy=dx\]         Integrating, we get \[{{y}^{2}}=x+c\]         This passes through \[(4,3)\], \ \[9=4+c\] Þ \[c=5\]                 Hence the equation of the curve is \[{{y}^{2}}=x+5\].


You need to login to perform this action.
You will be redirected in 3 sec spinner