Q: An equation of the form

$\displaystyle t^{2}\frac{d^{2}y}{dt^{2}}+\alpha\\t\frac{dy}{dt}+ \beta\\y=0$, $\displaystyle t>0$ with $\displaystyle \alpha$ and $\displaystyle \beta$ real constants, is called an Euler equation.

a) Let $\displaystyle x=ln(t)$ and calculate $\displaystyle \frac{d^{2}y}{dt^{2}}$ and $\displaystyle \frac{dy}{dt}$ in terms of $\displaystyle \frac{d^{2}y}{dx^{2}}$ and $\displaystyle \frac{dy}{dx}$.

My question is, what funtion am I differentiating with respect x? Do I write $\displaystyle y=t=e^{2}$ and differentiat that? What is the function y that I am differentiating?