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D/dx Ce^x - x - 1

  1. Sep 3, 2009 #1
    I read this in my calculus first year textbook, and Im just curious.

    1. The problem statement, all variables and given/known data
    For differential equation dy/dx = x + y, the general solution is y = Ce^x - x -1 (the solution of which is beyond this course). Verify this by solving dy/dx.


    2. Relevant equations
    calculus equations


    3. The attempt at a solution
    dy/dx = Ce^x - 1

    this looks nothing like x + y however. what am I missing?
     
  2. jcsd
  3. Sep 3, 2009 #2
    x + y = x + Ce^x-x-1=Ce^x-1

    Simply substitute your solution into the original differential equation to verify.
     
  4. Sep 3, 2009 #3
    Thanks! At least it's a trivial solution, which kind of makes me feel better, but not really =]
     
  5. Sep 4, 2009 #4
    I will do the same on this way:

    y' = x+y

    y=Ce^x - x -1

    y'=Ce^x-1

    Ce^x-1=y+x

    y=Ce^x-1-x
     
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