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Problem 1 Easy Difficulty

In Problems $1-8,$ classify the equation as separable, linear, exact, or none of these. Notice that some equations may have more than one classification.
$$\left(x^{2} y+x^{4} \cos x\right) d x-x^{3} d y=0$$


not exact.. not separable $\dots$ but it's linear.


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Video Transcript

in this video, we're gonna go through the answer to question number one from chapter 2.4. So ask to classify whether the equation here is inseparable, linear, exact or none of these. Okay, First, let's, uh, see whether it is separable s O. If it's separable, then we can write it as some function. G off X times by D. X plus some function Hey, age of why times by d Why equals era? Uh, not clearly. We can't do that. Yes, we can put this X on this side, but there's no way Thio put this. Why? On its own? Ah, on this side. Because we basically have a term containing why Aditya term not containing why so you can't base put those two up. So it is not several isat linear. Ah, yes, it is linear. That's because you condone, um quite easily Write it as, uh let's see to it, right Asked me why t x, um minus X. Why is equal to X gives minus one of eggs? Why? I mean minus X Cossacks on this is in the form needed to be linear, as in there's only terms continued. Why? Andi want Jax Thanks. So it is Lydia. Uh, that is exact. Well, let's see. So Well, let's look at the M, the md. Why? So this is day 50. Why, off the first term, which is X squared y plus extra for cause X won't write that down. You could see that from the previous page, but the wide derivative is gonna be X squared. Uh, let's look at the end of the ex. This is minus X cubed. So the ex relative of that is gonna be minus three. Next squared. These two are equal to each other. Therefore, this equation is no exactly.