I have equation of type: a x^2 y(x)'' + bxy(x)' + cy = d(x) it is called, in my text book, a second order Euler equation. They say that I need to put $e^t$ instead of $x$ and than $Y(x(t))=y(x)$
After this, they write that it is clear that: \begin{align} x\frac{dy}{dx}&=\frac{dY}{dt}\\ (x^2)y'' &= \frac{d^2Y}{dt^2}-\frac{dY}{dt} \end{align} Please tell me what are they doing here.
thanks.