A Series Solution Comparison

for various degree approximations

Truncated series solutions are graphed below.

>	ode:=(v+5)*diff(y(v),v,v)-3*diff(y(v),v)-3*(y(v))=0;

>

Order:=7;

>	dsolve({ode,y(0)=0,D(y)(0)=2},y(v),type=series);

>

rhs(%);

>	poly:=convert(%,polynom);

>	with(plots):

Warning, the name changecoords has been redefined

>	Order7soln:=plot(poly,v=0..5,color=red):

>	display(Order7soln);

>	Order:=12;

>	dsolve({ode,y(0)=0,D(y)(0)=2},y(v),type=series);

>

rhs(%);

>	poly:=convert(%,polynom);

>	SeriesSoln:=plot(poly,v=0..5,color=blue):

>	display(SeriesSoln,Order7soln);

>	Order:=18;

>	dsolve({ode,y(0)=0,D(y)(0)=2},y(v),type=series);

>

rhs(%);

>	poly:=convert(%,polynom);

>	SeriesSoln:=plot(poly,v=0..5,color=blue):

>	display(SeriesSoln,Order7soln);

>