The discussion revolves around the general solution of the differential equation dy/dt = -ay + b. Participants are exploring the steps involved in deriving the solution and verifying its correctness.
There is no consensus on the correctness of the solution or the verification method, as participants are still discussing the steps and assumptions involved.
Participants have not fully resolved the implications of their assumptions, particularly regarding the simplification of terms and the verification process for the solution.
Or ##y = Ce^{-at} + \frac b a##xavier777 said: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)
Substitute your solution in the original differential equation and you should get a true statement.xavier777 said: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 ?