If $u = \frac{1}{y}[\phi(ax + y) + \phi(ax - y)]$, and $\phi$ is twice differentiable, show that, $$\frac{\partial^2u}{\partial x^2} = \frac{a^2}{y^2}\frac{\partial}{\partial y}\left(y^2 \frac{\partial u}{\partial y}\right)$$
I arrived at the following:: $$LHS: \frac{a^2}{y}\left(\partial_x^2\phi(ax + y) + \partial_x^2\phi(ax - y)\right)$$ $$RHS: \frac{a^2}{y}\left(\partial_y^2\phi(ax + y) + \partial_y^2\phi(ax - y)\right)$$
After this how to show $LHS = RHS$?