Consider the equation of motion

\[\frac{d^{2} u}{d \varphi^{2}}+u-\frac{1}{p}=3 \lambda u^{2}\]

where \(p\) and \(\lambda\) are constants. Find the solution using perturbation theory to first order in the small parameter \(\lambda\). Assess whether your approximate solution is a good one by solving the problem using numerical techniques and comparing with your result from the first order perturbation method.