Series Solution Take-Home Number 4

With initial conditions

Truncated series solutions are graphed in blue (Order = 8), red (Order = 12), green (Order = 16), and black (Order = 32) .

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

>

Order:=8;

>	dsolve({ode,y(2)=0,D(y)(2)=3},y(x),type=series);

>

rhs(%);

>	poly1:=convert(%,polynom);

>	with(plots):

>	SeriesSoln1:=plot(poly1,x=2..7,color=blue):

>	display(SeriesSoln1);

>	Order:=12;

>	dsolve({ode,y(2)=0,D(y)(2)=3},y(x),type=series);

>

rhs(%);

>	poly2:=convert(%,polynom);

>	SeriesSoln2:=plot(poly2,x=2..7,color=red):

>	display(SeriesSoln1,SeriesSoln2);

>	Order:=16;

>	dsolve({ode,y(2)=0,D(y)(2)=3},y(x),type=series);

>

rhs(%);

>	poly3:=convert(%,polynom);

>	SeriesSoln3:=plot(poly3,x=2..7,color=green):

>	display(SeriesSoln1,SeriesSoln2,SeriesSoln3);

>	soln1:=plot(poly1,x=2..7,y=0..100,color=blue):

>	soln2:=plot(poly2,x=2..7,y=0..100,color=red):

>	soln3:=plot(poly3,x=2..7,y=0..100,color=green):

>	display(soln1,soln2,soln3);

>	Order:=32;

>	dsolve({ode,y(2)=0,D(y)(2)=3},y(x),type=series);

>

rhs(%);

>	poly4:=convert(%,polynom);

>	with(plots):

>	SeriesSoln4:=plot(poly4,x=2..7,color=black):

>	display(SeriesSoln4);

>	soln4:=plot(poly4,x=2..7,y=0..100,color=black):

>	display(soln1,soln2,soln3,soln4);

>