$\dfrac{d^2y}{dt^2}=\dfrac{d}{dt}\left(\dfrac{1}{t } \dfrac{dy}{dx}\right)=$

$-\dfrac{1}{t^2}\dfrac{dy}{dx}+\dfrac{1}{t}\dfrac{d} {dt}\left(\dfrac{dy}{dx}\right)=$

$-\dfrac{1}{t^2}\dfrac{dy}{dx}+\dfrac{1}{t}\dfrac{d} {dx}\left(\dfrac{dy}{dt}\right)=$

$-\dfrac{1}{t^2}\dfrac{dy}{dx}+\dfrac{1}{t}\dfrac{d} {dx}\left(\dfrac{dy}{dx}\dfrac{dx}{dt}\right)=$

$-\dfrac{1}{t^2}\dfrac{dy}{dx}+\dfrac{1}{t^2}\dfrac{ d}{dx}\left(\dfrac{dy}{dx}\right)=$

$-\dfrac{1}{t^2}\dfrac{dy}{dx}+\dfrac{1}{t^2}\dfrac{ d^2y}{dx^2}=$

$\dfrac{1}{t^2}\left(\dfrac{d^2y}{dx^2}-\dfrac{dy}{dx}\right)$