## Boundary value problem for the heat equation...

Hello!! Please help me,I need to solve a system of linear algebraic equations by running, and I solved the built-in command solve

```restart;
with(plots):
f:=unapply(-x^2+1,x);
mu[1]:=unapply(1/(t^2+1),t);
mu[2]:=unapply(1/(t-5),t);
g:=unapply(t^3-7*x,[t,x]);
l:=2; T:=3;
n:=10: m:=n:
h:=evalf(l/n);
tau:=evalf(T/m);
for k from 0 to n do
x[k]:=h*k:
end do:
for j from 0 to m do
t[j]:=tau*j:
end do:
ss:=evalf({seq(seq((y[k,j+1]-y[k,j])/tau=(y[k-1,j]-2*y[k,j]+y[k+1,j])/h^2+g(t[j],x[k]),k=1..n-1),j=0..m-1),seq(y[0,j]=mu[1](t[j]),j=1..m),seq(y[k,0]=f(x[k]),k=0..n),seq(y[n,j]=mu[2](t[j]),j=1..m)});
#s:=evalf(solve(ss,{seq(seq(y[k,j],k=0..n),j=0..m)}));
```

## How to get more graphs with given sequence ?...

We know the following facts:

The SequenceGraph command returns a graph with the specified degree sequence given as input, if such a graph exists. It raises an exception otherwise.
But  If I  want to get more graphs  that satisfy this condition of degree sequence ? (If graphs are not many ,I want get all graphs better)
what should I do.?
For example: DrawGraph(SequenceGraph([3, 2, 2, 1, 1, 1]));  It returns the first graph below, but it is obvious that the second graph also fits the condition.

squenceGraph.mw

## I encountered syntax error of a differential equat...

 > restart:
 > # # Define gamma as local (don't like doing this!) #   local gamma:local pi: # # Replaced 'indexed' parameters with 'inert subscript' # parameters - otherwise one gets a problem defining # both the unindexed 'phi' and the indexed phi[c] #   M__h := 100: beta__o := 0.034: beta__j := .025: mu__1 := 0.0004:   epsilon := .7902: alpha := 0.11: psi := 0.000136: phi := 0.05:   omega := .7: eta := .134: delta := .245: f := 0.21:   M__v := 1000: beta__k := 0.09:   mu__v := .0005: M__c := .636:   beta__g := 0.15: mu__c := 0.0019: pi :=0.01231: theta := 0.12: mu__e := 0.005 # # D() is Maple's differential operator replated D(T) # with DD(T) in the following to avoid confusion #   ODE1 := diff(B(T), T) = M__h-beta__o*B(T)-beta__j*B(T)-mu__1*B(T)+epsilon*G(T)+alpha*F(T):   ODE2 := diff(C(T), T) = beta__o*B(T)*J(T)-beta__j*C(T)-(psi+mu__1+phi)*C(T):   ODE3 := diff(DD(T), T) = beta__j*B(T)*L(T)- beta_o*E(T)-(omega+mu__1+eta)*DD(T):   ODE4 := diff(E(T), T) = beta_o*E(T)-beta__j*C(T)-(delta+mu__1+eta+phi)*E(T):   ODE5 := diff(F(T), T) = psi*C(T)-(alpha+mu__1)*F(T)+f*delta*E(T):   ODE6 := diff(G(T), T) = omega*DD(T)-(epsilon+mu__1)*G(T)+(1-f)*delta*E(T):   ODE7 := diff(H(T), T) = M__v-beta__k*H(T)-mu__v*H(T):   ODE8 := diff(J(T), T) = beta__k*H(T)-mu__v*J(T):   ODE9 := diff(K(T), T) = M__c-beta__g*K(T)-mu__c*K(T):   ODE10:= diff(L(T), T) = beta__g*K(T)-mu__c*L(T):   ODE11:= diff(M(T), T) = pi*(DD(T)+ theta*E(T))-mu__e*M(T):   B0 := 100: C0 := 90: D0 := 45: E0 := 38:   F0 := 10: G0 := 45: H0 := 50: J0 := 70: K0 :=20: L0:= 65: M0 :=22: # # Solve system #   ans := dsolve( { ODE1, ODE2, ODE3, ODE4, ODE5, ODE6, ODE7, ODE8,                    B(0) = B0, C(0) = C0, DD(0) = D0, E(0) = E0,                    F(0) = F0, G(0) = G0, H(0) = H0, J(0) = J0, K(0) = K0, L(0) = L0, M(0) = M0,                  },                  numeric                ); # # Plot solutions for a few of the dependent variablss # just to show everything is working (more-or-less!) #   plots:-odeplot( ans, [T, B(T)], T=0..5);   plots:-odeplot( ans, [T, C(T)], T=0..5);   plots:-odeplot( ans, [T, DD(T)], T=0..5);   plots:-odeplot( ans, [T, E(T)], T=0..5);   plots:-odeplot( ans, [T, F(T)], T=0..5);   plots:-odeplot( ans, [T, G(T)], T=0..5);   plots:-odeplot( ans, [T, H(T)], T=0..5);   plots:-odeplot( ans, [T, J(T)], T=0..5);   plots:-odeplot( ans, [T, K(T)], T=0..5);   plots:-odeplot( ans, [T, L(T)], T=0..5);   plots:-odeplot( ans, [T, M(T)], T=0..5);
 >

## Collect equation...

Hello Dear,

I have the following equation

This equation is satisfied if the coefficients are zero.

So I need an order in Maple to write that

## solution of the differential equation by the Milne...

Good evening!!! I have a task to implement the task of Cauchy by the method of Milne, wrote the code, but did not understand it until the end, help to understand? what's wrong?
First calculate four "initial" values by the method of Runge-Kutta methods, then use the method of Milne, the Fact that two times running, perhaps extra?

```restart;
with(plots):
a:=0; b:=1; eps:=evalf(10^(-3)):
f:=unapply(2*x*(x^2+y),x,y);
G:=simplify(dsolve({diff(y(x),x)=f(x,y(x)),y(a)=1}));
N:=15: h:=(b-a)/N:
for i from 0 to N do
x[i]:=a+i*h:
end do:
y[0]:=1;
s[0]:=1;
for i from 0 to 2 do
t[1]:=evalf(h*f(x[i],y[i])):
t[2]:=evalf(h*f(x[i]+h/2,y[i]+t[1]/2)):
t[3]:=evalf(h*f(x[i]+h/2,y[i]+t[2]/2)):
t[4]:=evalf(h*f(x[i]+h,y[i]+t[3])):
y[i+1]:=evalf(y[i]+(t[1]+2*t[2]+2*t[3]+t[4])/6):
q[1]:=evalf(h*f(x[i],s[i])):
q[2]:=evalf(h*f(x[i]+h/2,s[i]+q[1]/2)):
q[3]:=evalf(h*f(x[i]+h/2,s[i]+q[2]/2)):
q[4]:=evalf(h*f(x[i]+h,s[i]+q[3])):
s[i+1]:=evalf(s[i]+(q[1]+2*q[2]+2*q[3]+q[4])/6):
end do;
for i from 3 to N-1 do
y[i+1]:=evalf(y[i-3]+((4*h)/3)*(2*f(x[i],y[i])-f(x[i-1],y[i-1])+2*f(x[i-2],y[i-2]))):
s[i+1]:=evalf(s[i-1]+(h/3)*(f(x[i+1],y[i+1])+4*f(x[i],s[i])+f(x[i-1],s[i-1]))):
d[i+1]:=abs(y[i+1]-s[i+1])/29:
if abs(d[i+1]) < eps then y[i]:=y[i]:
else y[i]:=s[i];
end if: end do;
s1:=plot(rhs(G),x=a..b,color=yellow):
s2:=pointplot({seq([x[k],y[k]],k=0..N)}):
display(s1,s2);```

## Maple can't simplify a simple expression?!?...

So I have this expression

f:=(coth(x)^(1/3)-tanh(x)^(1/3))*(coth(x)^(2/3)+tanh(x)^(2/3)+1)

which Maple can not simplify?

I need to do it like this

Is this actually true or what is happening here?

## Unique solution using pdsolve...

Hi

I have a first oder PDE, I use pdsolve I obtained a solution depend on function F

condition_unique_solution.mw

My question: The boundary condition  f(x,y) = 1 is supplied on the line y = k x, where k is a constant. For which k
does there exist a unique solution for f(x, y)?

## A problem. ...

Let there be an infinite sequence of real numbers: A=a[0], a[1], ... .
Let P = (n -> sum(a[i]*x^i, i=0..n)).
What is A if for all n: P(n) has n real roots.

## Plotting functions with units...

Hi there

I'm an old user of Maple, but I've never been able to plot functions with unit. You can see my latest attempt down below

```b := 120*Unit('mm');
h := 200*Unit('mm');
V := 8*Unit('kN');

I__x := (1/12)*b*h^3

Q(x):=(1/2)*((1/4)*h^2-(100*Unit('mm')-x)^2)*b
tau(x):=V*Q(x)/(I__x*b)

plot(Q(x(Unit('mm')), units), x = 0*Unit('mm') .. 100*Unit('mm'))
```

Plot_function_with_units.mw

If anyone is able to help me with this problem, I would greatly appreciate it.

## Maple 18: laplace in annular domain...

Hi

I solve the laplace equation written in polar coordinates in annular domain.
The code run without any error

But there is no solution displayed after running the code, note that I use Maple 18

Laplace_annulardomain.mw

## Assign for loop - Matrix change into Table in for ...

I want to divide each row of Marix A by diagonal element. In for loop, when I assign dividing results to the letter , the type of A still remains matrix, but if I choose another letter (like B) results are stored in Table. Why? How can I assign to a matrix?

Also I can't figure out why maple doesn't show elements of table(see worksheet file).

I should notice that my main problem is assigning not dividing.

worksheet.mw

## Can not generate Matlab code...

Hi everyone;

I want to generate the Matlab code from the Maple code but I obtained an error message as shown below. Can anyone tell me please what does this error message mean?

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Thank you ^^

## How to write codes using maple to stimulate all de...

i want to design a packaging container to hold 320 sphere-shaped chocolates that each has a diameter 1.8 cm and weights about 3.2g each. i hope can get all posible shape using maple18 .

## Can not calculate a defined integral ...

Good morning everyone,

I have a problem, when I try to evaluate the definite integral below, Maple can not provide a result. What can I do so that the Maple can calculate this integral?

This is the Maple code with the result:

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 (1.1)
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Thank you !