Sure! So on the first one, the suggested substitution is $x=e^t$. The reason this works is because the original DE is a Cauchy-Euler equation, where you're multiplying each derivative by successively lower powers of $x$. So, if we do this substitution, we need all the derivatives in place (note here that $y'=dy/dx$ and $\dot{y}=dy/dt$):
\begin{align*}
x&=e^t \\
\frac{dx}{dt}&=e^t \\
\frac{dt}{dx}&=e^{-t} \\
y'&=\frac{dy}{dx}=\frac{dy}{dt} \, \frac{dt}{dx} = \dot{y} \, e^{-t} \\
y''&=\frac{d^{2}y}{dx^{2}}=\frac{d}{dx} \, \frac{dy}{dx} = \left[\frac{d}{dt} \, \frac{dy}{dx}\right] \frac{dt}{dx}
=\frac{d}{dt}\left[ \dot{y} \, e^{-t} \right] e^{-t}
=\left[ \ddot{y} e^{-t} - \dot{y} e^{-t} \right] e^{-t} = e^{-2t} (\ddot{y}-\dot{y}).
\end{align*}
Now, substitute all this stuff into the original DE. What do you get?