solx=x/.Solve[wx^2+(1/4)x^4,x]​​{xA,xB}={solx[[3]],solx[[4]]}​​{xC,xM,xD}={solx[[3]],solx[[2]],solx[[4]]}​​{xE,xF}={solx[[2]],solx[[4]]}​​xG=1/Sqrt[2]
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xIII[t_]=2Sec[t];​​eq1=x[t]D[x[t],{t,3}]-D[x[t],{t}]D[x[t],{t,2}]==-D[x[t],{t}]x[t]^3
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With[{ww=10^(-2),tt=1},x0=xA/.www;​​x0p=Sqrt[ww-x0^2-(1/4)x0^4];​​x00p=-x0-(1/2)x0^3;​​x000p=-(3/2)(x0^2)x0p-x0p;​​xn=x[t]/.NDSolve[eq1&&(x[0]==x0)&&(x'[0]==x0p)&&(x''[0]==x00p),x[t],{t,0,tt}];​​Plot[{xn,xIII[t]-2.1},{t,0,tt},PlotRange{-0.5,0.5},PlotLabel"Numerical solution of ODE eq: \nblue curve = numerical solution\nyellow curve = symbolic solution",AxesLabel{"t","x(t)"}]]