Stitching Solutions
For
\( y' = 2e^{x}\sqrt{|y|} \)
three solutions pass through \( (0,0) \):
\( y=(e^{x}-1)^{2}, \quad y=-(e^{x}-1)^{2}, \quad y \equiv 0. \)
Because uniqueness fails on \( y=0 \), pieces may be stitched at any junction where both value and slope agree — every stitched curve is again a solution, and every solution is non-decreasing.
