Lindstedt
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Consider a non-linear oscillator governed by the differential equation x''(t) - ϵx[x'(t)] + x = 0, where the initial conditions are given by x(0)=xo and v(0)=0. Employ the Lindstedt method to expand up to the second order. Specifically, determine the three sets until the order of ϵ^2. Next, calculate the values of ω1 and ω2, and use them for x(t) up to the 2nd order.
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