MapleDEfield.mws

Slope Fields

For Various Differential Equations

>    restart:with(DEtools):

>    DirField:=dfieldplot(diff(y(x),x)=y(x)*cos(x),y(x),x=0..6.28,y=-3.14..3.14,color=BLUE,arrows=MEDIUM,axes=BOXED):

>    with(plots): 

Warning, the name changecoords has been redefined

>    soln1:=plot(exp(sin(x)),x=0..6.28,y=0..3.14,color=red,thickness=2):

>    soln2:=plot(-exp(sin(x)),x=0..6.28,y=0..3.14,color=red,thickness=2):

>    soln3:=plot(0.4*exp(sin(x)),x=0..6.28,y=0..3.14,color=red,thickness=2):

>    soln4:=plot(-0.4*exp(sin(x)),x=0..6.28,y=0..3.14,color=red,thickness=2):

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

[Maple Plot]

>    restart:with(DEtools):

>    DirField:=dfieldplot(diff(y(x),x)=(y(x)*exp(-x)-sin(x))/(exp(-x)+2*y(x)),y(x),x=0..10,y=-1..2,color=BLUE,arrows=MEDIUM,axes=BOXED):

>    with(plots):

>    display(DirField);

[Maple Plot]

>    DirField:=dfieldplot(diff(y(x),x)=2*y(x)/x+sin(3*x)*x^2,y(x),x=1.57..8,y=-90..90,color=BLUE,arrows=MEDIUM,axes=BOXED):

>    with(plots):

>    display(DirField);

[Maple Plot]

Here is an animation of solutions for various initial conditions.

>    animate((-1/3)*(x^2)*cos(3*x)+(4*t/3.14^2)*x^2,x=1.57..8,t=-3..3,frames=13);

[Maple Plot]

>    SolnPics:=animate((-1/3)*(x^2)*cos(3*x)+(4*t/3.14^2)*x^2,x=1.57..8,t=-3..3,thickness=2,frames=13):

>    display(DirField,SolnPics);

[Maple Plot]

>    DirFieldb:=dfieldplot(diff(y(x),x)=2*y(x)/x+sin(3*x)*x^2,y(x),x=1.57..8,y=0..65,color=BLUE,arrows=MEDIUM,axes=BOXED):

>    Solnb:=plot((-1/3)*(x^2)*cos(3*x)+(8/Pi^2)*x^2,x=Pi/2..8,y=0..65,thickness=2):

>    display(DirFieldb,Solnb);

[Maple Plot]

>    DirField2:=dfieldplot(diff(y(x),x)=0.01*y(x)*(100-y(x)),y(x),x=0..20,y=-10..110,color=BLUE,arrows=MEDIUM,axes=BOXED):

>    Soln2:=plot(100*exp(x)/(9+exp(x)),x=0..20,y=-10..110,thickness=2):

>    display(DirField2,Soln2);

[Maple Plot]

>    DirField3:=dfieldplot(diff(y(x),x)=y(x)/x+(y(x)/x)^2,y(x),x=1..4,y=-40..40,color=BLUE,arrows=MEDIUM,axes=BOXED):

>    Soln3:=plot(x/(1-ln(x)),x=1..4,y=-40..40,thickness=2):

>    display(DirField3,Soln3);

[Maple Plot]

>    DirField4:=dfieldplot(diff(y(x),x)=(y(x)*exp(-x)-sin(x))/(exp(-x)+2*y(x)),y(x),x=0..20,y=-1..2,color=BLUE,arrows=MEDIUM,axes=BOXED):

>    Soln4:=plot((-exp(-x)+sqrt(exp(-2*x)+4*cos(x)+4))/2,x=0..20,y=-1..2,thickness=2):

>    display(DirField4,Soln4);

[Maple Plot]

>    DirField5:=dfieldplot(diff(y(x),x)=(y(x)*exp(-x)-sin(x))/(exp(-x)+2*y(x)),y(x),x=0..8,y=0..1.5,color=BLUE,arrows=MEDIUM,axes=BOXED):

>    Soln5:=plot((-exp(-x)+sqrt(exp(-2*x)+4*cos(x)+4))/2,x=0..8,y=0..1.5,thickness=2):

>    display(DirField5,Soln5);

[Maple Plot]

>    DirField6:=dfieldplot(diff(y(x),x)=(y(x)*exp(-x)-sin(x))/(exp(-x)+2*y(x)),y(x),x=2.8..3.4,y=0..0.3,color=BLUE,arrows=MEDIUM,axes=BOXED):

>    Soln6:=plot((-exp(-x)+sqrt(exp(-2*x)+4*cos(x)+4))/2,x=2.8..3.4,y=0..0.3,thickness=2):

>    display(DirField6,Soln6);

[Maple Plot]

>    DirField7:=dfieldplot(diff(y(x),x)=(y(x)*exp(-x)-sin(x))/(exp(-x)+2*y(x)),y(x),x=3.1..3.18,y=0..0.02,color=BLUE,arrows=MEDIUM,axes=BOXED):

>    Soln7:=plot((-exp(-x)+sqrt(exp(-2*x)+4*cos(x)+4))/2,x=3.1..3.18,y=0..0.02,thickness=2):

>    display(DirField7,Soln7);

[Maple Plot]

>    DirField8:=dfieldplot(diff(y(x),x)=(y(x)*exp(-x)-sin(x))/(exp(-x)+2*y(x)),y(x),x=6.24..6.32,y=1.4128..1.4134,color=BLUE,arrows=MEDIUM,axes=BOXED):

>    Soln8:=plot((-exp(-x)+sqrt(exp(-2*x)+4*cos(x)+4))/2,x=6.24..6.32,y=1.4128..1.4134,thickness=2):

>    display(DirField8,Soln8);

[Maple Plot]

>    DirField9:=dfieldplot(diff(y(x),x)=(2*y(x)*sin(x)-3)/cos(x),y(x),x=0..4*Pi,y=-10..10,color=BLUE,arrows=MEDIUM,axes=BOXED):

>    Soln9:=plot((1-3*sin(x))/(1-(sin(x))^2),x=0..4*Pi,y=-10..10,thickness=2):

>    display(DirField9,Soln9);

[Maple Plot]

>    DirField10:=dfieldplot(diff(y(x),x)=(2*y(x)*sin(x)-3)/cos(x),y(x),x=Pi/2..3*Pi/2,y=-10..10,color=BLUE,arrows=MEDIUM,axes=BOXED):

>    Soln10:=plot((1-3*sin(x))/(1-(sin(x))^2),x=Pi/2..3*Pi/2,y=-10..10,thickness=2):

>    display(DirField10,Soln10);

[Maple Plot]

>