Hi all,

I'm trying to use logplot but it's very time consuming. Any suggestion please!

Cheers!

restart:with(plots):

S1:=x+x^2*Sum(t^(k*alpha+1)/GAMMA(k*alpha+2),k=0..infinity);

S2:=x+x^2*Sum(t^(k*alpha+1)/GAMMA(k*alpha+2),k=0..n);

alpha:=0.75:x:=0.5:n:=10:

logplot(abs(S1-S2),t=0..1);

Hello!

To get the phase portrait, I did this

Eq1:=diff(x(t),t)=1-d*x(t)-x(t)*v(t);

Eq2:=diff(y(t),t)=-a*y(t)+x(t)*v(t)-y(t)*w(t);

Eq3:=diff(z(t),t)=-b*z(t)+y(t)*w(t);

Eq4:=diff(v(t),t)=-p*v(t)+y(t);

Eq5:=diff(w(t),t)=-q*w(t)+c*z(t);

d:=0.012:a:=0.93:c:=40:b:=5.6:p:=5.6:q:=5.6:
ics:=x(0)=5,y(0)=1,z(0)=2,v(0)=0.5,w(0)=4;

eq1:=1-d*x-x*v;
eq2:=-a*y+x*v-y*w;
eq3:=-b*z+y*w;
p:=5.6:
eq4:=-p*v+y;
eq5:=-q*w+c*z;

solve({eq1=0,eq2=0,eq3=0,eq4=0,eq5=0},{x,y,z,v,w});

initialset:={seq(seq(seq(seq(seq([x(0)=a1,y(0)=a2,z(0)=a3,v(0)=a4,w(0)=a5],a1=0..5),a2=0..1),a3=0..2),a4=0..0.5),a5=0..4)}:

A:=DEplot([Eq1,Eq2,Eq3,Eq4,Eq5],[x(t),y(t),z(t),v(t),w(t)],t=0..140,x=5..7,y=0..2,initialset,stepsize=0.01,color=blue,linecolor=magenta,arrows=medium,axes=boxed):

Error, (in DEtools/DEplot/WhichPlot) More than two dependent variables - please indicate the desired scene.

I want phase portrait projected on x − y plane.

Any comments?

Is it possible to solve DDE with dsolve?

restart:

Eq1 := diff(x(t), t) = 1-.1*x(t)-0.5e-3*x(t)*v(t)/(1+0.1e-5*v(t));

Eq2 := diff(y(t), t) = 0.5e-3*x(t-10)*v(t-10)/(1+0.1e-5*v(t-10))-.3*y(t)-y(t)*z(t);

Eq3 := diff(v(t), t) = 200*y(t-10)-8*v(t);

Eq4 := diff(z(t), t) = 2*y(t)*z(t)-.15*z(t);

ics := x(0) = 1, y(0) = 1, v(0) = 5, z(0) = 1;

Thanks

restart:

Eq1:=x=(phi*(theta[m]-1/x)/theta[m]+(1-phi)/2);

solve({Eq1},x);

x := (1/4)*(phi*theta[m]+theta[m]+sqrt(phi^2*theta[m]^2+2*phi*theta[m]^2-16*phi*theta[m]+theta[m]^2))/theta[m];

Now plotting the first root

p1:=plot(subs(phi=0,x),theta[m]=0..14,color=red):
p2:=plot(subs(phi=0.1,x),theta[m]=0..14,color=green,linestyle=2):
p3:=plot(subs(phi=0.5,x),theta[m]=0..14,color=blue,linestyle=3):
p4:=plot(subs(phi=1,x),theta[m]=0..14,color=black):
display({p1,p2,p3,p4},axes=boxed,view=[0..14,0..1]);

Note: I'm unable to reproduce the following plot. Any idea?

 SA.mw

restart:

Eq2 := diff(T(y), y, y)+(diff(sigma(y), y))*(diff(T(y), y))+(diff(T(y), y))^2+(exp(-y)

+exp(y))^2 = 0;

Eq3 := diff(sigma(y), y, y)+(diff(T(y), y, y))= 0;

bcs2:=T(h1)=0,T(h2)=1,sigma(h1)=0,sigma(h2)=1;

dsolve({Eq2,Eq3,bcs2});

This give me nothing. Please help me out.