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A differential equation question

  1. May 26, 2014 #1
    There is differential equation with initial condition perplexing me.

    y'+ y = 1, y = ce^-x + 1 , y = 2.5 when x = 0

    First I take derivative of y which is -ce^-x then I sum it up with y which is -ce^-x+ce^-x + 1 equals 1 which is in harmony with y' + y = 1 but it
    seems that this is independent from integral constant c and so there are infinite number of c but in the answer c is -1.5.

    Have a nice day.
     
  2. jcsd
  3. May 26, 2014 #2
    ?
    y=1+c*e^(-x); at x= 0, y = 1+c*e° = 1+c=2.5, .....so, c = 1.5
     
    Last edited: May 26, 2014
  4. May 26, 2014 #3
    Thank you.
     
  5. Jun 1, 2014 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You were told, when they said "y= ce^{-x}+ 1" that this would satisfy the differential equation for all values of c. That is what that means. The problem was to find c such that y(0)= 2.5.
     
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