begin{equation}
  label{eqgeralds}
   a(x)y'' + b(x)y' + c(x)y = 0
end{equation}

begin{subequations}
   label{tgeraleqs}
   begin{align}
      label{tgeraleqs1}    (ay'')^{(n)} =& sum_{i=0}^{n}binom{n}   {i}a^{(i)}y^{(2+n-i)} \
       label{tgeraleqs2}   (by')^{(n)} =& sum_{i=0}^{n}binom{n}{i}b^{(i)}y^{(1+n-i)} \
       label{tgeraleqs3}   (cy)^{(n)} =& sum_{i=0}^{n}binom{n}{i}c^{(i)}y^{(n-i)}
    end{align}
end{subequations}

begin{subequations}
   label{eqsc}
   begin{align}
      (by')^{(n)} =& sum_{i=1}^{n}binom{n}{i-1}b^{(i-1)}y^{(2+n-i)}\
      (cy)^{(n)} =& sum_{i=2}^{n}binom{n}{i-2}c^{(i-2)}y^{(2+n-i)}
   end{align}
 end{subequations}