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MaplePrimes Activity

These are replies submitted by zhuxian


I answer by myself.

It will be right if we use the command


It is strange, and I don't know the reason.

Maple is silly.

@Carl Love



with(PDEtools)with(DifferentialGeometry)with(JetCalculus); with(DEtools)

Euc > 

DGsetup([t, x], [u], J, 10)

`frame name: J`

J > 

LL := L(t, x, u[], u[1], u[2])

L(t, x, u[], u[1], u[2])

J > 

G := EulerLagrange(LL)[1]

diff(L(t, x, u[], u[1], u[2]), u[])-(diff(diff(L(t, x, u[], u[1], u[2]), t), u[1]))-(diff(diff(L(t, x, u[], u[1], u[2]), u[]), u[1]))*u[1]-(diff(diff(L(t, x, u[], u[1], u[2]), u[1]), u[1]))*u[1, 1]-2*(diff(diff(L(t, x, u[], u[1], u[2]), u[1]), u[2]))*u[1, 2]-(diff(diff(L(t, x, u[], u[1], u[2]), x), u[2]))-(diff(diff(L(t, x, u[], u[1], u[2]), u[]), u[2]))*u[2]-(diff(diff(L(t, x, u[], u[1], u[2]), u[2]), u[2]))*u[2, 2]

J > 

eqs := {coeffs(G, {u[1, 1], u[1, 2], u[2, 2]})}; nops(eqs)


J > 

eqs := {coeffs(G*u[1, 1]+G, {u[1, 1], u[1, 2], u[2, 2]})}; nops(eqs)

Error, invalid arguments to coeffs





Download ques.mw

The second to last command is normal, but the last one is wrong.



@Christian Wolinski 

What do you mean '1D'?

The expression is obtained from

1. compute the EulerLagrange equation of L(t,x,u[],......);

2. some other computations, like addition and differential.

I just copied the expression from output of Maple.

@Carl Love 

Thanks for your help.

I changed a computer and it is normal. I don't know what is the matter with my computer.

Anyway, thanks for your work.


Thanks for your help!

I have tried this command, and it works.

However, there are too many solutions, and I want to select some interesting solutions.

There are too many constants (>30) in solution, and they are the form _C1, _C2, _C3, ..., _C35.

I want to set all but one to zero, how to do that?

Thanks for your time.


I learn much from your answer. Thanks!

The command "infolevel" is good.

However, how can I get the general solution?

I think maple has find the general solution, but it didn't stop, and continued to build some special solution.

How can I stop it, or other ideas to get the general solution?

For the file I upload, can you help me to get the  results?

Thank you very much. 


I forgot plus _C1 to the real_sol, since you can see that k starts from 2 in the constant C_k!

Thanks for that.

However, what I want is the general solutions of the differential equations through maple.

As you can see, the maple-solution is just a special solution.

That A(x,t) satisfies a linear differential equaiton is enough, not a special A(x,t)=C1exp(c1x)C2exp(t/C1).

How can I get the general solution, not by hand?

I will meet some other similiar problems,  I don't want to compute by hand each time, and actually I even don't trust the command 'pdsolve', for that there may be some solutions are hidden!



any advice or commence?




any advice or commence?


@Markiyan Hirnyk 

the result i get:

{_eta[u](x, t, u) = _C1*u+_C2, _xi[t](x, t, u) = _xi[t](x, t, u), _xi[x](x, t, u) = 2*(Int(diff(_xi[t](x, t, u), u), u))+(1/2)*(Int(-4*(Int(diff(_xi[t](x, t, u), x, u), u))-_C1+4*(diff(_xi[t](x, t, u), x)), x))+Int(3*_C1+_C2-2*(Int(-(Int(diff(_xi[t](x, t, u), x, u, t), u))+diff(_xi[t](x, t, u), x, t), x))-2*(Int(diff(_xi[t](x, t, u), u, t), u))+2*(diff(_xi[t](x, t, u), t)), t)+_C3}

window10 and maple 18.02

i decide to update maple.

i solved the system by hand, and it is not too complicated.

i don't know why infinite integrals appear in the results from maple.

maybe we shouldn't rely on the computer too much.


thank you for your comprehensive answer!

how to solve the system consist of the coefficients?

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