I was tasked to find the second derivative of the equation $2y = x^{2}y - 10$.
I tried solving it in two ways: using implicit differentiation and isolating $y$ in the equation.
If using implicit differentiation, I get $y'' = \frac{(2-x^{2})(2y + \frac{4x^{2}y}{2-x^{2}}) + 4x^{2}y}{(2-x^{2})^{2}}$.
If isolating $y$, since $y=\frac{-10}{2-x^{2}}$, I get $y''=\frac{-20(3x^{2} + 2)}{(2-x^{2})^{3}}$.
Since I am getting different answers, is there a "more correct" way of approaching this problem? It was not specified that we should use implicit differentiation.