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

JEE Main & Advanced Mathematics Differential Equations Question Bank Critical Thinking

  • question_answer
    The differential equation representing the family of curves \[{{y}^{2}}=2c(x+\sqrt{c}),\]where c is a positive parameter, is of [IIT 1999; AIEEE 2005; MP PET 2002]

    A) Order 1                                     

    B) Order 2

    C) Degree 3

    D) Degree 4

    Correct Answer: A

    Solution :

    • Given curve is \[{{y}^{2}}=2c\text{ }(x+\sqrt{c}).\]                   
    • Differentiate w.r.t. x, \[2y\frac{dy}{dx}=2c\]Þ\[c=y\frac{dy}{dx}\]       
    • Hence differential equation is       
    • \[{{y}^{2}}=2y\frac{dy}{dx}\left( x+\sqrt{y\frac{dy}{dx}} \right)\] Þ \[\frac{y}{2dy/dx}-x=\sqrt{y\frac{dy}{dx}}\]       
    • Squaring and multiplying by \[{{\left( \frac{dy}{dx} \right)}^{2}}\]       
    • \[y{{\left( \frac{dy}{dx} \right)}^{3}}-{{x}^{2}}{{\left( \frac{dy}{dx} \right)}^{2}}+xy\left( \frac{dy}{dx} \right)-\frac{{{y}^{2}}}{4}=0\]                   
    • Hence order is 1 and degree is 3.


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