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Looking at the source of desolve the difference is in how the variable tempic is set, namely the offending expression is (dvar==ics[1])._maxima_():

sage: (y == e)._maxima_()
%e='y(_SAGE_VAR_t)

versus

sage: (y == 1*e)._maxima_()
'y(_SAGE_VAR_t)=%e

So it seems that the interface to Maxima cannot be trusted to preserve the ordering LHS = RHS of an equation. This looks like a bug to me, which should be reported.

Looking at the source of desolve the difference is in how the variable tempic is set, namely the offending expression is (dvar==ics[1])._maxima_():

sage: (y y == e)._maxima_()
%e='y(_SAGE_VAR_t)
e
e == y(t)

versus

sage: (y y == 1*e)._maxima_()
'y(_SAGE_VAR_t)=%e
1*e
y(t) == e

So it seems that the interface to Maxima Sage cannot be trusted to preserve the ordering LHS = RHS of an equation. This looks like is definitely a bug to me, which should be reported.