Substitute z(x)=∑ n=0
[infinity]
​
a n
​
x n
into z ′′
+xz ′
+z=x 2
+4x+3 and equate the coefficients of like powers of x on both sides of the equation to find the first four nonzero terms in a power series expansion about x=0 of a general solution to the differential equation. z(x)=+⋯ (Type an expression in terms of a 0
​
and a 1
​
that includes all terms up to order 3.)