SturmLiouville Form. A second-order equation is said to be in SturmLiouville form if it is expressed as $$\left[p(t) y^{\prime}(t)\right]^{\prime}+q(t) y(t)=0$$ Show that the substitutions $x_{1}=y, x_{2}=p y^{\prime}$ result inthe normal form $$\begin{aligned} x_{1}^{\prime} &=x_{2} / p \\ x_{2}^{\prime} &=-q x_{1} \end{aligned}$$

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