Require:
First order ode \(F(x,y,y')=0\)
if \(f(x,y)\) analytic at \(x_0\) then 
Apply Taylor series defintion directly to find the series expansion. Let
else 
do something else
end if
if \(f(x,y)\) analytic at \(x_0\) then Apply Taylor series defintion directly to find the series expansion. Let else do something else end if