I  can't solve this series,please could you help me ,the maple code for this.

restart;
U[0](x):=(e)^(x);
                             exp(x)
n:=7:  for k from 0 to n do  U[k+1](x):=solve((k+1)U[k+1](x)-((∂)^2)/((∂)^( )x^2) U[k](x)-2 U[k](x));  end do;
Error, (in solve) cannot solve expressions with diff(diff(U[0](x), x), x) for x

How to rectify this error

k := 0;

for k[1] from 0 to k do Y[k[1]+3] := solve(sum(sum(factorial(k[1]+3)*(-1)^((k-k[1]-1)*(1/2))*Y(k[1]+3)/(factorial(k[1])*factorial(k-k[1])), k[1] = 0 .. k), k = 0 .. infinity)-(sum(1/4*((-1)^((1/2)*k)/factorial(k)-(3^k)(-1)^((1/2)*k)/factorial(k)), k = 0 .. infinity))-(sum(factorial(k[1]+2)*(-1)^((k-k[1])*(1/2))*Y(k[1]+2)/(factorial(k[1])*factorial(k-k[factorial(1)])), k[1] = 0 .. k)), Y[k[1]+3]) end do;
                               0
Error, (in sum) summation variable previously assigned, second argument evaluates to 0 = 0 .. k