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NDA2017MathematicsDifferential EquationsActual

If x d y=y(d x+y d y) ; y(1)=1 and y(x) 0 , then what is y(-3) equal to?

Options

  1. A3
  2. B2
  3. C1
  4. D0

Correct answer

A. 3

Step-by-step solution

aligned & x d y=y d x+y^2 d y & x d y d x =y+y^2 d y d x & y-x d y d x y^2 = -d y d x aligned Integrating both sides x y =-y+c Given, x =1, y =1 aligned & 1 1 =-1+ c & c =2 & x y + y =2 & x + y ^2=2 y & -3+ y ^2-2 y =0 & y ^2-2 y -3=0 & y =3,-1 & y =3 aligned

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