Why not just start by solving the DE:
via integrating factor and obtain the two solutions. What can you say about either solution at x=0?
Ok, then here's how I'd do (A):
and dividing by :
for which the integrating factor is so we have:
which the left side is the differential of so:
or:
and if then I can let and obtain the solution . However, if say for example, then I'd obtain which has no solution.
Ok, so I'm a little uneasy about dividing through by in the first step since this is valid if then obtain the solution and solve it for .