MapleDEseriesSolnExp.mws

>    ode:=diff(y(x),x,x,x)-x*diff(y(x),x,x)+x*diff(y(x),x)-y(x)=0;

ode := diff(y(x),`$`(x,3))-x*diff(y(x),`$`(x,2))+x*diff(y(x),x)-y(x) = 0

>    ans:=dsolve({ode,y(0)=1,D(y)(0)=1,D(D(y))(0)=1},y(x),type=series);

ans := y(x) = series(1+1*x+1/2*x^2+1/6*x^3+1/24*x^4+1/120*x^5+1/720*x^6+1/5040*x^7+1/40320*x^8+1/362880*x^9+1/3628800*x^10+1/39916800*x^11+1/479001600*x^12+1/6227020800*x^13+O(x^14),x,14)
ans := y(x) = series(1+1*x+1/2*x^2+1/6*x^3+1/24*x^4+1/120*x^5+1/720*x^6+1/5040*x^7+1/40320*x^8+1/362880*x^9+1/3628800*x^10+1/39916800*x^11+1/479001600*x^12+1/6227020800*x^13+O(x^14),x,14)

>