Question: Taylor Series for an Implicit Function

I am considering a function y(x) which is defined implicitly such that:

y(x):= x-> ln((1+x)*y) + exp(x^(2)*y^(2))

I am attempting to show that the Taylor series about x = 0 is:

y(x) = 1 - x^2 - (1/3)x^3 + (55/24)x^4 + (4/5)x^5 - (439/80)x^6 + O(x^7)

This could be done by using Maple to take derivatives up to sixth order and then substituting into the formula for the Taylor series.  My initial idea for the Taylor series was to use the identity 

ln((1+x)*y) + exp(x^(2)*y^(2)) = x + cos(x)

but obviously the RHS does not give the required form for the Taylor series about x = 0 (although I can use it to show that y(0) = 1).  Would it be possible to use Maple to take six derivatives of the left-hand side instead and then use that to create the Taylor series as far as sixth order?