This if of the form
In this occasion you find the integrating factor , but you can exclude the constant!
Then your solution is of the form:
Hence, given that
Applying conditions gives C = 4
Use long division and you should get the same as your textbook. Alternatively use inspection!
If , then
Clearly , so that the first terms in each bracket multiply to produce . must be , so that the last terms in each bracket multiply to give you . And to account for , must be !
Both you and your textbook were correct .