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