Figure 2From: A criterion for oscillations in the solutions of the polytropic Lane-Emden equations The numerical solutions of the spherical equation ( 8 ) with \(\pmb{D=3}\) , integer \(\pmb{n = 1-7}\) , and boundary conditions \(\pmb{y(0)=1}\) and \(\pmb{y'(0)=0}\) . For \(n=1\) and \(n=5\), the solutions are also known analytically [10]. Surprisingly, the solution for \(n=3\) is the only nonlinear solution that is oscillatory.Back to article page