i am trying to solve a complicated system of differential equations, which involves several hundred of equations. Luckily they can be all solved seperately, but there are to many to do it by hand. The first of them are of the form
$P1*A[x_1,x_2,x_3,x_4,x_5]+P2*B[x_1,x_2,x_3,x_4,x_5]+P3*C[x_1,x_2,x_3,x_4,x_5]+P4*D[x_1,x_2,x_3,x_4,x_5]+P5*E[x_1,x_2,x_3,x_4,x_5]=P6$
subject to
$B[x_1,x_2,x_3,x_4,x_5]=A[x_2,x_1,x_3,x_4,x_5]$,
$C[x_1,x_2,x_3,x_4,x_5]=A[x_3,x_2,x_1,x_4,x_5]$
$D[x_1,x_2,x_3,x_4,x_5]=A[x_4,x_2,x_3,x_1,x_5]$
$E[x_1,x_2,x_3,x_4,x_5]=A[x_5,x_2,x_3,x_4,x_1]$
where all the Pi are given Polynomials in the $x_i$. If this is not mathematical exact enough, the system is given by the equations 3.14-3.16 in https://arxiv.org/pdf/1606.07376.pdf The problem now is how to implement these constraints. Taking
$5 x1^4 A[x1, x2] + 5 x2^4 B[x1, x2] == x1^6 x2^6$
as a toy example,which is by hand easy to solve by $A=(x1^2*x2^6)/10$, I tried to insert the conditions directly in the equation, i.e.
DSolveValue[5 x1^4 A[x1, x2] + 5 x2^4 A[x2, x1] == x1^6 x2^6, A[x1, x2], {x1, x2}]
which does not work as it says the variables are not ordered correctly. Then I tried to implement it as a condition,
DSolveValue[
{5 x1^4 A[x1, x2] + 5 x2^4 B[x1, x2] == x1^6 x2^6,A[x1, x2] == B[x2, x1]},
A[x1, x2],
{x1,x2}]
DSolveValue[
5 x1^4 A[x1, x2] + 5 x2^4 B[x1, x2] == x1^6 x2^6, A[x1, x2],
{x1, x2},
DirichletCondition[A[x1, x2] == B[x2, x1], true]]
which also does not work as in the first case, It simply does nothing and in the second one says it cannot use the $x_i$ as variables. Is there a way to solve such problems in Mathematica?
