DSolve with Initial Conditions

Q: How can I solve the following ordinary differential equation?

[Graphics:inoutbgr2.gif][Graphics:inoutbgr1.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr3.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr4.gif]

Dropping the problematic initial condition, [Graphics:inoutbgr5.gif], we have

[Graphics:inoutbgr2.gif][Graphics:inoutbgr6.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr7.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr8.gif]

Applying [Graphics:inoutbgr9.gif] manually, we now determine [Graphics:inoutbgr10.gif]by implicit series expansion,

[Graphics:inoutbgr2.gif][Graphics:inoutbgr11.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr12.gif]

and obtain the solution to the original problem:

[Graphics:inoutbgr2.gif][Graphics:inoutbgr13.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr14.gif]