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lets say that I use perturbation theory but only up to order e^0 so that u_0=cossqrta_0t+1/sqrta_0sinsqrta_0t. then do i let u_0 = e^(mu*t)P(t) and solve

lets say that I use perturbation theory but only up to order e^0 so that u_0=cossqrta_0t+1/sqrta_0sinsqrta_0t. then do i let u_0 = e^(mu*t)P(t) and solve for mu

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