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$$ 2 t x d x+\left(t^{2}-x^{2}\right) d t=0 $$

$\frac{1}{2 t} x-\frac{t}{2} x^{-1}$

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in this video, we're gonna go through the answer to question number one from chapter 2.6. We asked to identify whether this equation is from a genius for new E linear coefficients Off Given four. Okay, so let's start the top. Let's figure out whether it's home a genius. Okay, so we can write it as let's see, we could write DX DT as one over two t x times by X squared minus T squares. Okay, so let's just rewrite this a little bit, so so we can divide the top and bottom of this fraction by T Squares. I already got one over two times. Exhibit C times X over tea squared minus one on this is a function of X over tea. So it's homogeneous equation make a right time green. Okay, Is that the new equation? But we could also write this right inside as one over to tea Times X minus tiu over too X two months. What? This isn't a TV for this guy is your p of X. This guy is your cue of X on DDE This minus one is your end succeed? That's written in binary form. It's certainly not linear because we have t squares and X squared. So whichever way you could, it's not gonna be linear. Um, and you can quite easily convince yourself that is no Oops. I should put across roughing it sick for linear, and you can quite easily convince yourself it is also not in the form given a question.

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