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Possible workaround :

sage: var("x, omega, t");
sage: u=function("u")
sage: def eq():return u(1)==cos(omega*t)
sage: eq()
u(1) == cos(omega*t)
sage: u(x)=e^(2*t*x)
sage: eq()
e^(2*t) == cos(omega*t)

But I fail to see the point...

HTH,