# Question:Is there something similar to solve/identity for dsolve? ODEs with independent variables.

## Question:Is there something similar to solve/identity for dsolve? ODEs with independent variables.

Maple 2019

Hello,

I am solving some overdetermined system of ODEs in cylindrical coordinates r,phi,Z. I obtain some equations of the following type:

`(diff(_F1(phi, Z), phi)*r + diff(diff(s_r(phi, Z), phi), phi))/r = -s_r(phi, Z)/r`

As can be seen, the differentiated functions do not depend on r, which is an independent variable. Thus, the correct solution is to separate the equation and have

`_F1(phi,Z)=_F1(Z), s_r(phi,Z)=s_r(Z).`

By using dsolve, I always obtain a solution containing r.

A similar problem that does no contain derivatives is solved by solve/identity.

Is there something similar for dsolve?

EDIT: I again put here more info and file. I solve some overdetermined system of differential equations.

```[diff(s_r(r, phi, Z), r) = 0, diff(s_r(r, phi, Z), phi) = -diff(s_phi(r, phi, Z), r)*r^2,
diff(s_Z(r, phi, Z), r) = -diff(s_r(r, phi, Z), Z), diff(s_phi(r, phi, Z), phi) = -s_r(r, phi, Z)/r,
diff(s_Z(r, phi, Z), phi) = -diff(s_phi(r, phi, Z), Z)*r^2, diff(s_Z(r, phi, Z), Z) = 0,
diff(m(r, phi, Z), r) = s_Z(r, phi, Z)*B_phi(r, phi, Z) - s_phi(r, phi, Z)*B_Z(r, phi, Z),
diff(m(r, phi, Z), phi) = s_r(r, phi, Z)*B_Z(r, phi, Z) - s_Z(r, phi, Z)*B_r(r, phi, Z),
diff(m(r, phi, Z), Z) = s_phi(r, phi, Z)*B_r(r, phi, Z) - s_r(r, phi, Z)*B_phi(r, phi, Z),
s_r(r, phi, Z)*diff(W(r, phi, Z), r) + s_phi(r, phi, Z)*diff(W(r, phi, Z), phi) +
s_Z(r, phi, Z)*diff(W(r, phi, Z), Z) = 0]```

After some time, I arrive at the equation in the original question. So the independance of the other functions on r is the consequence of the other equations.

Here is the file (shortened): mwquestion2.mw

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