Find all solutions to the equation $\displaystyle x^2 + y^3 = z^2,\ x>0,\ y>0,\ z>0,\ (x,y,z)=1$

not a clue where to start with this. The book does not say anything about what to do when the exponents do not match and I can not seem to find anything on any of the various math help sites. Maybe I am just not knowing what to search for, but I am stuck. Can anyone point me in the right direction? In what way would this differ from having all exponents = 2?