Please find below the problem $tobe$ solved using the Method $of$ Multiple Scales. The system $is$ not forced, $soit$ will $be$ only free vibrations

Nonlimer Hynamis

Use the Metted $of$ Multyle Cals $to$ solve

$x^{}+w_0^{2}x=-c{x}^{}-x^2{x}^{}$

Souter

Assinne

$x=x_0+x_1,$ where $i=\frac{d}{dx}={}_0+{}_1,{}_0=\frac{2s}{2s}$

$=\frac{2}{2T_1}$

ucto the differential gracter

fubstrute unto the differential gaaten