Find all solutions of the differential equation

on the interval . Prove that exactly one of these solutions is valid on the larger interval .

*Proof.* We apply Theorem 8.3 (page 310 of Apostol) with

Further, we choose and obtain solutions in terms of , this gives us

Therefore,

These are then all of the solutions valid on . The only one of these solutions valid on the interval is the one with , or

I found the following: f(x) = sinx + C/sinx, where C=b-1

I think the function is

or

where

The answer is slightly off: should be (b+1)/sinx + sinx , or C/sinx + sinx. cos(2*pi/2) is negative. So b=-1 ?

I’ve also found the following:

Same here