## Integral not evaluated...

In the following file when p is a fraction other than 1/2 the integral is not evaluated. Please help

 >
 (1)
 >

## How to find the solution of differential equations...

Can any one help to find the value of sigma(r,z) and theta(r,z) from the differential equations analytically,

ODEs:= <
diff(theta(r),r\$2) = -(1/r)*diff(theta(r),r) - diff(sigma(r),r)*diff(theta(r),r)-diff(theta(r),r)^2,
diff(sigma(r),r\$2) = -(1/r)*diff(sigma(r),r) -diff(theta(r),r\$2)-(1/r)*diff(theta(r),r)>;
boundary conditions

'diff((theta),r)=0','diff((sigma),r)=0'; # at r=0
and theta=0, sigma=0; #at r=h(z)

## how to find the solution...

help required to find the value of u analytically

## code for ODE Plot need some help...

restart:
ode:=-diff(y(x),x,x)+(1/4)*y(x)-4*exp(-x)=0:
init:=y(0)=0,y(1)=0:
exact:=dsolve({ode,init},y(x)):
N:=8:
trial:=sum(c[i]*x^i,i=1..N):
residual:=lhs(subs(y(x)=trial,ode)):
R:=simplify(residual):
sys:=[]:
for i from 1 to N  do sys:=[op(sys),int(R*x^i,x=0..1)=0];
od:
sys:
vars:=seq(c[i],i=1..N):
A,b:=LinearAlgebra[GenerateMatrix](sys,[vars]):
sol:=solve({op(sys)},{vars}):
assign(sol):
trial:

# if i am plotting the graph exact and trial i am getting the error, separately if i am plotting the graph of exact i am getting the plot, similarly exact - trial error
trial_fun:=unapply(trial,x):
exact_fun:=unapply(rhs(exact),x):
evalf(trial_fun(1)-exact_fun(1)):
plot(exact,trial,x=0..1):
Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct
plot(trial,x=0..1,legend['trial']):
Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

#error calculation

plot(exact-trial,x=0..1):
Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

restart:

restart:

Eqn:=-diff(y(x),x,x)+(1/4)*y(x)-4*exp(-x)=0:
BCs:=y(0)=0,y(1)=0:
dsolve({Eqn,BCs},y(x)):
assign(%):y:=unapply(y(x),x):
plot(y(x),x=0..1);

## maple13 is not executing the program...

Dear sir

I am facing the problem with executing the program with Maple13. The software problem is maple13 is not executing the programs and showing the dialogue box as waiting for the kernel. Actually, what is this kernel, which is not understanding me? So please can anyone do a favor in this regard? How to connect to the kernel?

## Warning, solutions may have been lost....

I need some help. I'm trying to solve this system of equations, but maple says the solutions may have been lost.

I don't know why. Here are the equations:

I have four equations,very unknown variables in the equation.

I am trying to solve for any 4 unknowns ,not must had be Zoo1.Zoo2.th1.th2,it can be Za1.Za2.Zb1.Zb2.

Any help  would be greatly appreciated.

## How to use a result of the function as a known par...

Пример02.mws

for example，i have already got the odeplot of function m(t),n(t).  And now i want to use the value of m(t) to calculate function x(t),y(t).

eq1:=diff(x(t),t)=m(t)*cos(y(t))-n(t)*sin(y(t));  #The function of x(t):

eq2:=diff(y(t),t)=m(t)*sin(y(t))+n(t)*cos(y(t));  #The function y(t):

inc:=x(0)=1;y(0)=2;

dsolve({eq1,eq2,inc},[x(t),y(t)],numeric);

but i got an Error

Error, (in dsolve/numeric/process_input) unknown m present in ODE system is not a specified dependent variable or evaluatable procedure.

But before this i have already got the odeplot of function m(t) and n(t),how can i solve this problem？

## Error problem in mapple...

Can anyone tell me why the following command

restart; with(plots): with(Statistics):  with(numapprox):

create an error of this type?

Error, Got internal error in Typesetting:-Parse : "cannot determine if this expression is true or false: membertype(specfunc(Typesetting:-mspace),Typesetting:-mempty(Typesetting:-mspace(depth = "0.0ex",height = "0.0ex",width = "0.0em",linebreak = "newline")))"

## To solve partial differential equation with numeri...

Hello everyone!

I have following system of partial differential equation and tried to solve with numerical method

pde1:=diff(U, t)-(diff(U, x, x))-2*U*(diff(U, x))+diff(U*V, x)

> pde2 := diff(V, t)-(diff(V, x, x))-2*V*(diff(V, x))+diff(U*V, x);
> ics := { U(x, 0) = sin(x),  V(x, 0) = sin(x)};

sol:=pdsolve(pde1,pde2,ics,numeric,time=t, range=1..20)

I am get following error

Error, (in pdsolve) invalid input: `pdsolve/numeric` expects its 2nd argument, IBCs, to be of type {set, list}, but received 0

## Why maple does not respond to the commands?...

I was calculating the total derivative of a function but maple does not respond to the commands like alias,diff,totaldiff etc.

## How do i get in plot line style to be of type line...

Dear sir, can we get a plot of graph with line style like  line+symbol so on..

I am attaching codes and sample graph .

h:=z->1-(delta2/2)*(1 + cos(2*(Pi/L1)*(z - d1 - L1))):
K1:=(4/h(z)^4)-(sin(alpha)/F)-h(z)^2+Nb*h(z)^4:
lambda:=(F,Nb,delta2)->Int(K1,z=0..1):

L1:=0.2:
d1:=0.2:
alpha:=Pi/6:
A:=plot( [seq(seq(lambda(F,Nb,delta2), Nb=[0.1,0.2,0.3]), F=[0.1,0.2,0.5])],
delta2=0.02..0.1, linestyle = [solid,longdash,dashdot],'
thickness = 2',color=[red\$3,blue\$3,black\$3],
legend=["Nb=0.1","Nb=0.2","Nb=0.3",""\$6]):
B:=plots:-textplot([[0.05,-1,F=0.1],[0.05,1.5,F=0.2], [0.05,3,F=0.5]], font=[times, 14]):

plots:-display(A, B);

## How do i get a legend only three curves in maple...

Dear sir i want to display only three curves 1, curve 2 curve 3  in legends but in the plot it should be nine curve a sampe codes and a sample graph is attaching , please give suggestions. Here is my codes

h:=z->1-(delta2/2)*(1 + cos(2*(Pi/L1)*(z - d1 - L1))):
K1:=(4/h(z)^4)-(sin(alpha)/F)-h(z)^2+Nb*h(z)^4:
lambda:=(F,Nb,delta2)->Int(K1,z=0..1):

L1:=0.2:
d1:=0.2:
alpha:=Pi/6:
A:=plot( [seq(seq(lambda(F,Nb,delta2), Nb=[0.1,0.2,0.3]), F=[0.1,0.2,0.5])], delta2=0.02..0.1, linestyle = [solid,longdash,dashdot],'thickness = 2',color=[red\$3,blue\$3,black\$3]):

B:=plots:-textplot([[0.05,-1,F=0.1],[0.05,1.5,F=0.2], [0.05,3,F=0.5]], font=[times, 14]):

plots:-display(A, B);
sample graphs

## contour plot different v alues...

Hellow sir how to plot stream lines for different values of alpha =6,7,8,9.

I am attaching the sample graph and codes.
How to get the output like that only.

eq1:= alpha*diff(f(eta),eta\$3)+f(eta)*diff(f(eta),eta\$2)-diff(f(eta),eta)^2+1:
eq2:= diff(h(eta),eta\$2)+f(eta)*alpha*diff(h(eta),eta)-diff(f(eta),eta)*h(eta):
eq3:= diff(H(eta),eta) = h(eta):
bc:= f(0)=0, D(f)(0)=0, D(f)(6)=1, h(0)=0, D(h)(6)=1, H(0)=0:
A1:= dsolve(
{eq||(1..3), bc},
numeric, method= bvp[midrich], abserr = 1e-10, output= operator
):

psi:= unapply(eval(x*f(eta)+H(eta), A1), (x,eta)):
plots:-contourplot((psi(x,eta), x= 0..6, eta= 0..6),alpha=6);