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MHT CET20242 May 2024Evening ShiftMathematicsDifferential EquationsActual

If y=y(x) is the solution of the differential equation ( 5+ e ^x 2+y ) d y ~d x + e ^x=0 satisfying y(0)=1 , then a value of y( 13) is

Options

  1. A-1
  2. B0
  3. C1
  4. D2

Correct answer

A. -1

Step-by-step solution

aligned & ( 5+ e ^x 2+y ) d y ~d x + e ^x=0 & ~d y 2+y = - e ^x 5+ e ^x ~d x aligned Integrating on both sides, we get aligned & |2+y|=- |5+ e ^x |+ | c | & |2+y|= | c 5+ e ^x | aligned Since y(0)=1 i.e., y=1 when x=0 aligned & 3= | c 6 | & 3= c 6 & c =18 & |2+y|= | 18 5+ e ^x | [ From (i) ] & 2+y= 18 5+ e ^x & y= 18 5+ e ^x -2 aligned aligned y( 13) & = 18 5+ e ^ 13 -2 & = 18 5+13 -2 & =-1 aligned

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