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Manipal MET2012MathematicsDifferential Equations

If x d y=y(d x+y d y), y(1)=1 and y(x) 0 . Then, y(-3) is equal to

Options

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

Correct answer

A. 3

Step-by-step solution

array ll x d y=y(d x+y d y), y 0 & x d y-y d x=y^2 d y & x d y-y d x y^2 =d y array -d ( x y )=d y On integrating both sides, we get x y =-y+C ....(i) As y(1)=1 x=1, y=1 C=2 Eq. (i) becomes x y +y=2 Again, for x=-3 array lr & -3+y^2=2 y & y^2-2 y-3=0 & (y+1)(y-3)=0 array As y 0 , we take y=3 , (neglecting y=-1 )

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