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Section 11.4, p. 560

We use the multiscale analysis \fs2 y(t)\sim Y_0(t, \epsilon t) for \fs2 \epsilon\to 0 with \fs2 Y_0(t,\tau) =A(\tau) e^{i\,{t\over 2}}+ A^*(\tau) e^{-i\, \theta(\tau)} \, e^{-i\,{t\over2}} for the Mathieu
equation \fs2 y''+\left[{1\over 4} + (a_1+2\, \cos t)\, \epsilon\right] y=0. Show that \fs2 |a_1|=1 is the limit for the stability of the equilibrium \fs2 y=0.