# Setup equations

eqn_sys := {cos(t)*sin(t)^2*cos(x)+sin(t)*cos(t)^2*sin(x)+D[1,1](y)(t,x)+y(t,x)=0}:

parameters := [{y(t,x)}], ivars = {t, x}:

ind_vars := {t}:

# Works as expected

depends_ind_vars :=
Not(
  And(
    unknown,
    satisfies(f -> indets({op(f)},assignable) intersect ind_vars = {})
  )):

good := frontend(':-pdsolve', [eqn_sys],
  [{`+`,`*`,depends_ind_vars}], parameters):

#frontend(print, [eqn_sys],
#  [{`+`,`*`,depends_ind_vars}], parameters):

# Doesn't work

depends_ind_vars :=
Not(
  And(
    satisfies(f -> indets({op(f)},assignable) intersect ind_vars = {})
  )):

bad := frontend(':-pdsolve', [eqn_sys],
  [{`+`,`*`,depends_ind_vars}], parameters):

#frontend(print, [eqn_sys],
#  [{`+`,`*`,depends_ind_vars}], parameters):

# Compare solutions

rhs(good[1]) - rhs(bad[1]):
expand(%):
combine(%,trig);