text: # Is this general solution correct?
  
  • I
  xavier777
  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)
  
  ## Answers and Replies
  
  Mentor
  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)
  Or ##y = Ce^{-at} + \frac b a##
  Did you check to see if your solution satisfies the diff. equation?
  
  xavier777
  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 ?
  
  Mentor
  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 ?
  Substitute your solution in the original differential equation and you should get a true statement.