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Application of modified wavelet and homotopy perturbation methods to nonlinear oscillation problems

): x ( t ) = C T ψ ( t ) $$\begin{array}{} \displaystyle x(t) = {C^T}\psi (t) \end{array}$$ (34) Homotopy perturbation method : Solving the nonlinear Eq. (27) using a new approach of homotopy perturbation method, we get x ( t ) = l cos t + sin 2 t 2 2 α l 2 3 + β l 3 4 cos ⁡ t + β l 3 8 cos 2 t + 4 α l 2 3 + β l 3 8 $$\begin{array}{} \displaystyle x(t) = l\,\cos \,t + {\sin ^2}\left( {\frac{t}{2}} \right)\,\left[ {\,\left( {\frac{{2\alpha \,{l^2}}}{3} + \frac{{\beta {l^3}}}{4}} \right)\cos t + \frac{{\beta \,{l^3}}}{8}\cos \,2t + \frac{{4\alpha {l^2}}}{3

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