Compute the following multiple integral exactly and/or with 10 correct significant digits

Int( exp( - add(x[i],i=1..10)^3), seq(x[i]=0..1, i=1..10) );

The problem is suggested by a previous post.

I try to find the exact (symbolic) value of

(-2*sqrt(7)-4)*EllipticK((1/8)*sqrt(2)*(-3+sqrt(7)))^2+4*EllipticE(-(1/8)*sqrt(2)*(-3+sqrt(7)))*sqrt(7)*EllipticK((1/8)*sqrt(2)*(-3+sqrt(7)))

I tried 'simplify' with different options and 'convert'. It would be pi=3.141... as numerical approximation suggests.

Many thanks.

EF.3.mwHi, I want to ask that how to find the exact solution of equation without applying any technique

Hello,

Good day.

How to avoid float(undefined) for v3, v4,v5 in this problem.

Thank you in advance.

Try_for_Second_Grade_Fluid.mw

hello,

restart:

ODE:=diff(T(z),z$2)+A1*(S-1/L+1/L*exp(-L*z))*diff(T(z),z)+A2*T(z)=0;

bcs:=T(0)=1,T(infinity)=0;

bcs:=T(0)=1,T(A3)=0;

dsolve({ODE,bcs});

where, A1, A2, A3, L, S are all constants.

i get an exact solution but is there any way around to get a more compact solution?

hey friends am stuck with some code. My code is correct and am trying to find exact solution but not able to see output. Please kindly check it and let me know exact_solution.mw

hi friends am using maple 13 which is unable to find exact solutions for pdes

because for exact solution i should have maple 15 but am not able to install that so please can anyone of u can find exact sloution for me of the pde

pde := diff(U(x, y), x, x)-3*(diff(U(x, y), y, y))+16 = 0 where boundary conditions are

U=0 on x=1,-1

diff(U(x, y), y) = -U on y=1, -1< x

diff(U(x, y), y) = U on y=-1, -1< x

Hi friends. Am trying to plot a graph that shows the difference between cubic spline, crank

nicolson and exact soution in 2d through this command but am not able to get it.

Whereas table is mentioned below at t=0.05

x cubic crank exact0.05 0.0879 0.0855 0.07560.15 0.2514 0.2446 0.21940.25 0.3807 0.3708 0.34170.35 0.4625 0.4512 0.43050.45 0.4928 0.4815 0.47730.55 0.4747 0.4646 0.47330.65 0.4151 0.4609 0.4305

Can we find exact solution of PDE with help of maple?

If it is yes the please let me how to write commands for parabolic pde

u_{t}=k u_{xx} with boundary conditions u(0,t)=u(l,t)=0 and initial condition u(x,0)=e^{-x}

consider:

assume(k[f1]>0,k[f2]>0,k[f2]>k[f1],h_bar>0,m>0);

h_bar:=1.0545e-34;m:=0.10938e-31;n[0]=1e28;> eq1:=n=(k[f1]^3+k[f2]^3)/6/Pi^2;> eq2:=e*V=h_bar^2/2/m*(k[f2]^2-k[f1]^2);

> solve({eq1,eq2},{k[f1],k[f2]});

in the final command i get a very messy numerical&symbolic results like

{k[f1] = 1016612041.* (-1.*RootOf(9456017282782496601177464289*n^2*Pi^4...

Hi

I am usign dsolve for maple to give my a fuction z(t) . Maple solves the differential equation but i want maple to give me the exact number for specific t values z(60) and so on. But maple is given as an answer z(60) and not a number

Can someone help me to generate the same, identical grpah over several periods in x-axis? In exact term, I mean that I need to plot a periodical grpah, that repeats itself over the interval? It is like given a periodical function and now have to draw it many times...(function can be any form, not only sine and cosine)

Like when I type

1/2^2;

it gives

1/4

but if I type

0.5^2;

0.25

I want it to consider 0.5 as 1/2, because sometimes I make computations on large equations and I want to have access to the symbolic output, not the numeric output.

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