Maple 11 Questions and Posts

These are Posts and Questions associated with the product, Maple 11

Hi,

Consider the following planar dynamical system(PDS) with parameters r, p1, s, n:
a:=(r+1)*(1+p1*s)/(2*(1-P1))-1/(n^2);
b:=(r+1)*(3-r)*(1-p1*s^2)/(8*(1-p1))-3/(2*n^4);
c:=(r+1)*(3-r)*(5-3*r)*(1+p1*s^3)/(48*(1-p1))-5/(2*n^6);
 

 

Hellow everyone,

Consider the following diffrential equation:

(dA(x)/dx )^2+V(A)=0,
1- How to plot dA/dx vs A?

2- How to find the coordinate of intersection point of f(x)=e-b*exp(x)-c*(1-2*x/c)^(1/2) with df/dx? e,b,c are constants.

 

 

Considering the follwoing expr:

A(x):=mue+(mun/gama)+(u0^2)-mud*x-mue*exp(x)-(mun/gama)*exp(gama*x)-(u0^2)*(1-2*x/u0^2)^(1/2);

where 

mue:=1/(1+alpha+beta);
mun:=alpha/(1+alpha+beta);
mud:=beta/(1+alpha+beta);
u0:=(mue+mun*gama)^(-1/2);
 and assuming the values of alpha and beta lie between 0.1..0.6 and gama=15 ro 20.

How do I determine those values of (alpha,beta,gama) satisfying conditions [(3), (4)], [(3), (5)] or [(3),(6)]?

conditions:

A(x[m] <> 0) = 0:

where x_m is an extreme point of A(x) (other than x=0),

d*A(x)/dx, x = x[m] < 0:

d*A(x)/dx, x = x[m] > 0:

d*A(x)/dx, x = x[m] = 0:

Hi,
How do I simplify the following polynomial:

 -(729 beta (1/2 (-1/9 (-5/27 beta-1/9) lambda^6-1/9 (1/9 beta^2 TT+(10/9 TE+2/3 TT) beta-1/9 TE) lambda^4+5/27 (2/5 TT (3/2 TT+TE) beta+TE (TE-2/5 TT)) beta lambda^2-1/9 TE beta^2 TT (-TT+TE)) p1(m,t)^2+(beta TT-1/3 lambda^2)^2 (-1/3 lambda^2+TE)^3 ((p2(m,t))/(lambda^2-3 TE)+3/2 ((lambda^2+TE) p1(m,t)^2)/((lambda^2-3 TE)^3))))/((3 beta TT-lambda^2)^3 (3 TE-lambda^2)^2),

as follows:

-3*beta*p2(m,t)/(lambda^2-3*beta*TT)+3*beta^2*(5*lambda^2-3*beta*TT)*p1(m,t)^2/(2*(lambda^2-3*beta*TT)^3)
?

I want to solve the following system of PDEs with Maple: 

In fact, I want to determine q1,n1,p1,nn1,qn1,pn1 as a functions of pphi1 (assume  ne1(X,T)=(alpha/(2))*pphi1(X,T))

(mu, nu, beta, lambda, TE , alpha and TT are constant, but q1,n1,p1,nn1,qn1,pn1 depend on (X,T))

How do I do that?             

                   
> diff(q1(X, T), X)-lambda*(diff(n1(X, T), X)) = 0;

diff(pphi1(X, T), X)+TE*(diff(p1(X, T), X))-lambda*(diff(q1(X, T), X)) = 0;

-lambda*(diff(p1(X, T), X))+3*(diff(q1(X, T), X)) = 0;

-lambda*(diff(nn1(X, T), X))+diff(qn1(X, T), X) = 0;

-lambda*(diff(qn1(X, T), X))+beta*TT*(diff(pn1(X, T), X))-beta*(diff(pphi1(X, T), X)) = 0;

-lambda*(diff(pn1(X, T), X))+3*(diff(qn1(X, T), X)) = 0;

-mu*ne1(X, T)-nu*nn1(X, T)+n1(X, T) = 0;

 

 

 

How can I transform the following differential equation from (x,t) to (X,T) coordinate, where, for example, X=x-alpha*t, T=beta*t (alpha and beta are constant)

diff(z, t)+(diff(R, x))*L+A*(diff(L, x))+diff(k, x, x)-(diff(k, t, t)) = 0

Thanks.

Suppose two following Eqs.:

(1) du/dt+d(u*w)/dx=0

(2) dw/dt+wdw/dx=0

I want to expand u(x,t) and w(x,t) in the power series of epsilon

u=u0+epsilon*u1+epsilon^2*u2+…

w=w0+epsilon*w1+epsilon^2*w2+…

and change the variables x,t to X,T as follows

 X=(x-alpha*t) and T=beta*t,

and solving Eqs. (1) and (2) for different order of epsilon (epsilon, epsilon^2, epsilon^3,…) to finding u0,w0,u1,w1,…

How do I do that?

Thanks.

 

d/dt(n_2)+d/dx (n0u2)

Thanks

With the following command I can plot two spheres and plot them.

f1 := x^2+y^2+z^2 = 1

f2 := x+y+z = 1

with(plottools);

with(plots);

S1 := implicitplot3d(f1, x = -1 .. 1, y = -1 .. 1, z = -1 .. 1, style = patchnogrid, color = blue, scaling = constrained, axes = boxed)

S2 := implicitplot3d(f2, x = -1 .. 1, y = -1 .. 1, z = -1 .. 1, style = patchnogrid, color = gold, scaling = constrained, axes = boxed)

dispaly(S1,S2)

My questions are:

1- How can I display (highlight) the circle which is the intersection between these two sphere on the same figure?

2- How can I find the equation of this circle?

Thank you.

ifactor(8650368) produces

                                                        2503  *  2^7 * 3^3

 

how can I produce the output with factors in order from small to large and printed f rom left

 

2^7 * 3^3 * 2503

 

Hi 

I have 3 equations

eq1 := vs = (Rs+Z)*i1+Z*i3

eq2 := A*vi = Z*i1+(Z+Rf+ro)*i3

eq3:= vo = (Rf+Z)*i3+Z*i1

 

and I want to solve for vo/vs . How to do that ?

the expected solution is 

Please help me to solve this integration

restart; with(LinearAlgebra); int(exp(-(ln(z/(snr*B^2))+4*sigma^2)^2/(32*sigma^2))*eta^2*(y/z)^((1/2)*eta^2-1)/(z*sqrt(32*Pi*sigma^2)*(2*sqrt(y*z))*(2*A[o]^(eta^2))), z, z = y/A[o]^2 .. infinity);

 

 

 

restart; with(LinearAlgebra); int(exp(-(ln(z/(snr*B^2))+4*sigma^2)^2/(32*sigma^2))*eta^2*(y/z)^((1/2)*eta^2-1)/(z*sqrt(32*Pi*sigma^2)*(2*sqrt(y*z))*(2*A[o]^(eta^2))), z, z = y/A[o]^2 .. infinity)

I'm trying to execute the program, which can be found here http://www.maplesoft.com/support/help/Maple/view.aspx?path=examples/pdsolve_boundaryconditions , but it does not work. I copied exactly what is written there:

restart; with(PDEtools):
U := diff_table(u(x,t)):
pde[1] := U[t]+c*U[x]=-lambda*U[];
bc[1] := eval(U[], t=0) = phi(x);
sys[1] := [pde[1], bc[1]];
pdsolve(sys[1]);

But after last command it just sais that

Error, (in pdsolve/sys/info) found functions with same name but depending on different arguments in the given DE system: [u(x,t), u(x,0)]

What's wrong?

Dear Community Members,

 

We have problem with calculation in Maple v11 and v18. when we make a calculation by using maple v11 and v18, we was not able to get the solution as you see enclosed. when we clicked to "enter + ; ", programme does not run.

 

Hello

I have a loop with the do structure but there is an error in the loop .

how can I continue the loop by error or disregard it?

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