Dear Sir or Madam,
I would be grateful if you can help me to solve the the below question. The system is non-linear, I guess maybe the Picard-lindelof theorem will be helpful for this question.

Given the system
y'_1=xy_1-y_2,\ y_1(0)=1
y'_2=xy^2_1-y_2,\ y_2(0)=1
Show that the solution can be obtained for |x|<0.3 by successive
approximations.