Differential Equations · JEE Main previous year questions

2005 2 questions

1. Q342005 · 28 Apr 2005 · Shift 1

   The differential equation representing the family of curves $y^2=2c\left(x+\sqrt{c}\right)$, where $c>0$, is a parameter, is of order and degree as follows:

   1. A.order 1, degree 2
   2. B.order 1, degree 1
   3. C.order 1, degree 3
   4. D.order 2, degree 2
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   Answer: C

2. Q352005 · 28 Apr 2005 · Shift 1

   If $x\frac{dy}{dx}=y(\log y-\log x+1)$, then the solution of the equation is :

   1. A.$y\log \left(\frac{x}{y}\right)=cx$
   2. B.$x\log \left(\frac{y}{x}\right)=cy$
   3. C.$\log \left(\frac{y}{x}\right)=cx$
   4. D.$\log \left(\frac{x}{y}\right)=cy$
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   Answer: C