Obtain the approximate solution of period (2 pi) for the equation ({ }^{43}) [ ddot{x}+Omega^{2} x-varepsilon x^{2}=Gamma

Question:

Obtain the approximate solution of period \(2 \pi\) for the equation \({ }^{43}\)

\[
\ddot{x}+\Omega^{2} x-\varepsilon x^{2}=\Gamma \cos t, \quad \varepsilon>0
\]

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