# Question:Odetest only partially simplifies system of equations

## Question:Odetest only partially simplifies system of equations

Maple 2018

Hello,

I am attempting to check solutions to a system of ODEs using odetest. However, odetest only appears to partially substitute the provided solution. Furthermore, it appears to be related to the alphabetical order of the functions.

For instance, here I have two functions, phiL and phiM, that satisfy Laplace's equation and are coupled through the boundary conditions, BCs.

```laplace := {-phiL(z) + diff(phiL(z),z\$2)=0, -phiM(z) + diff(phiM(z),z\$2)=0}:
BCs := {phiL(d1)=0,phiM(-d1)=0,phiL(0)=phiM(0), D(phiL)(0)-D(phiM)(0)=-n}:
sol := {
phiM(z) = n/2/coth(d1)*(cosh(z)+coth(d1)*sinh(z)),
phiL(z) = n/2/coth(d1)*(cosh(z)-coth(d1)*sinh(z))
}:

odetest(sol, laplace union BCs,{phiL(z),phiM(z)});```

This returns

`{0, 1/2*(2*phiL(0)*coth(d1)-n)/coth(d1), D(phiM)(0)-1/2*n}`

Here, phiL(0) and phiM(0) are unevaluated even though the provided solutions are valid there.

Furthermore, while renaming phiL to an alphabetically earlier name (eg, phiJ) causes the corresponding change in the output. However, renaming it to something alphabetically after phiM (eg, phiN) causes the terms in the output to switch. That is, changing phiL to phiN in the above code results in

`{0, 1/2*(2*phiM(0)*coth(d1)-n)/coth(d1), D(phiN)(0)+1/2*n}`

Therefore, it seems to be related to the way Maple internally stores the list of variables.

Is this a bug? Or is there something I'm missing?

Thanks!

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