I'm having problems solving this exercise:
Prove that, if $x(t)=t^\alpha y(t), \alpha\in\mathbb{R}$ satisfies: $$0=t^2x''(t)+tp(t)x'(t)+q(t)x(t) \quad \forall t \in (0,r) $$ where $r>0$ is the radius of convergence of $y$ and $p$ and $q$ are analytic at $0,$ then $z(t)=(-t)^\alpha y(t)$ satisfies $$0=t^2z''(t)+tp(t)z'(t)+q(t)z(t) \quad \forall t \in (-r,0).$$
Any help? I assume that I must change my variable $t$ to $-t$ but I'm not sure how to solve the problem then.