Here's a procedure that should always work. Start with the equation . For convenience, replace the variable x by t, so that y is a function of t: . Integrate both sides from 0 to x: , or .
The idea now is to start with an approximate solution which you substitute into the integral, getting a new function which you then substitute into the integral to get another function , and so on.
The first approximation is just the constant function 1 (because this is given as the value of y at x=0). Then
. So . Next,
, and so on.