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Problem 8 Easy Difficulty

Sturm Liouville Form. A second-order equation is said to be in Sturm Liouville form if it is expressed as
$$\left[p(t) y^{\prime}(t)\right]^{\prime}+q(t) y(t)=0$$

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Video Transcript

So this is known as the Sturm Little Form, and we know that this form is the form of a second order equation. Remember, Second Order is referring to, um, a double derivative, uh, single derivative constant. So it's said to be in this form if it's expressed as the following. So we have p of T. Why prom of T All that prime plus q of t y t equals zero. And let's just understand why this is. That's because since this is on the outside, what we have now is essentially a chain rule or product rule more. We have p prime of T y prime of t plus p of t. Why double prime of T plus q of t y t. So then, Obviously it's not in this form anymore, but it is a second order equation because this is a second derivative right here.