Let \[ y=\sum_{n=0}^{\infty} a_{n} x^{n-1} \] be a solution of the equation \[ x^{2} y^{\prime \prime}+4 x y^{\prime}+(x+2) y=0 \text { for } x>0, \text { near } x_{0}=0 . \] If \[ a_{2}=-c a_{3} \] t