;

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 .