$2{{x}^{2}}+3{{y}^{2}}=1\Rightarrow f\,:\,2{{x}^{2}}+3{{y}^{2}}-1=0\Rightarrow {y}'=\frac{{{{{f}'}}_{x}}}{{{{{f}'}}_{y}}}=\frac{4x}{6y}=\frac{2x}{-3y}$ $\Rightarrow {y}''=\frac{6y-6x{y}'}{9{{y}^{2}}}=-\frac{6(y-x{y}')}{9{{y}^{2}}}=-\frac{2(y-x(-\frac{2x}{3y}))}{3{{y}^{2}}}=-\frac{2(3{{y}^{2}}+2{{x}^{2}})}{9{{y}^{3}}}=-\frac{2(1)}{9{{y}^{3}}}=-\frac{2}{9}\times \frac{1}{{{y}^{3}}}$