Is this general solution correct?

[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)

 

[Mark44]

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 e^Ce^-at = Ce^-at ?

 

[Mark44]

How do I do that? Differentiate it to get back to the original diff eq ? If yes, then what about the assumption e^Ce^-at = Ce^-at ?

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