Apply the picard iteration to the first-order equation

Question

Apply the picard iteration to the first-order equation

$x'=2t-2 \sqrt{max(0,x)} \,\, , x(0)=0 $.

Does it converge?

In this case should we separate in cases"$x>0$ and $x<0$ ", and resolve the ODEs separately, or should we use another strategy?