Write the ODE as
and truncate as many terms as needed to obtain only the terms up to order 4:
We only care about the coefficients up to
, so we take the system
Now, we're given initial values
and 
, so that
which gives
and truncate as many terms as needed to obtain only the terms up to order 4:
We only care about the coefficients up to
Now, we're given initial values
which gives