MapleDESeriesTH.mws

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

ode := diff(y(x),`$`(x,2))+x*diff(y(x),x)+y(x) = sin(x)

>    Order:=12;

Order := 12

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

y(x) = series(1*x-1/6*x^3+1/40*x^5-17/5040*x^7+1/2688*x^9-1349/39916800*x^11+O(x^12),x,12)

>    rhs(%);

series(1*x-1/6*x^3+1/40*x^5-17/5040*x^7+1/2688*x^9-1349/39916800*x^11+O(x^12),x,12)

>    poly:=convert(%,polynom);

poly := x-1/6*x^3+1/40*x^5-17/5040*x^7+1/2688*x^9-1349/39916800*x^11

>    with(plots):plot(poly,x=0..3,color=blue); 

Warning, the name changecoords has been redefined

[Maple Plot]

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