Hello everybody,

I am new to MaplePrimes, so I am sorry for possible bad formatting.

I am solving some physical problem in cylindrical coordinates, so the EDIT **independent** variables are r,phi,Z. The equations I obtain contain constants _C from dsolve and constant parameters aplha[i,j], for example

I would like to solve this type of equations for all values of the variables, namely phi in the example above.

If I do not choose the variables for which to solve, I get phi=phi as one of the equations in the solution. If i choose all the variables except phi, i get an the expression for the constants containing the variable phi.

Is there a way to solve these equations automatically or do I have to separate them manually using collect and coeffs?

Or could the solution be the comand Parameters from Physics package?

Thank you in advance for your help.

EDIT: I did not explain the problem properly. I am solving some complicated set of determining equations to obtain integrals of motion. They are *rce *in the attached file. I substitute some ansatz for the magnetic field and I solve them for

The first set of equation, called *third *in the file are solved by *HOconds_polar_solved. *This is where the konstants alpha[i,j] appear. I substitute *HOconds_polar_solved* into the equations *rce *and try to solve them for the remaining functions.

Because it is an overdetermined system, I get some equations of the type in the original question or (for example)

8*r^5*_C1*((alpha[4, 4] - alpha[5, 5])*cos(2*phi) + sin(2*phi)*alpha[4, 5])=0

Because r and phi are the **independent** veriables of the system, the solution to the equation above should be

_C1=0 or (alpha[4,4]=alpha[5,5] and alpha[4,5]=0)

But I get the following.

solve(8*r^5*_C1*((alpha[4, 4] - alpha[5, 5])*cos(2*phi) + sin(2*phi)*alpha[4, 5]));
{_C1 = 0, phi = phi, r = r, alpha[4, 4] = alpha[4, 4], alpha[4, 5] = alpha[4, 5], alpha[5, 5] = alpha[5,5]},
{_C1 = _C1, phi = phi, r = 0, alpha[4, 4] = alpha[4, 4], alpha[4, 5] = alpha[4, 5], alpha[5, 5] = alpha[5, 5]},
{_C1 = _C1, phi = phi, r = r, alpha[4, 4] = -tan(2 phi) alpha[4, 5] + alpha[5, 5], alpha[4, 5] = alpha[4, 5], alpha[5, 5] = alpha[5, 5]}

The file (part of the original file, which is very long): question.mw

EDIT 2: I changed the title to contain independent variables, which makes the answer more clear. The second Answer from Carl Love works fine, at least in the presented case.