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I Is this general solution correct?

  1. Jun 20, 2016 #1
    Question : General solution of dy/dt = -ay + b
    My solution :

    dy/dt = -a(y-b/a)
    (dy/dt)/(y-(b/a)) = -a

    Integrating both sides :
    ln | y-(b/a) | = -at + C
    e(-at+C) = y-(b/a)
    Ce(-at) = y-(b/a)
     
  2. jcsd
  3. Jun 20, 2016 #2

    Mark44

    Staff: Mentor

    Or ##y = Ce^{-at} + \frac b a##
    Did you check to see if your solution satisfies the diff. equation?
     
  4. Jun 20, 2016 #3
    How do I do that? Differentiate it to get back to the original diff eq ? If yes, then what about the assumption eCe-at = Ce-at ?
     
  5. Jun 21, 2016 #4

    Mark44

    Staff: Mentor

    Substitute your solution in the original differential equation and you should get a true statement.
     
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