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Problem 3 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.
$$\sqrt{-2 y-y^{2}} d x+\left(3+2 x-x^{2}\right) d y=0$$

Answer

The equation is separable, it is not a linear function of y neither with y as independant. The equation is not exact

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Video Transcript

in this video, we're gonna go through the answer to question number three from chapter 2.4. So we asked Thio classify this equation acceptable. Exact Ah, a linear owned one of these. So I start with the question of set of whether it's separable, um is quite clearly separable because we can just put this guy on the bottom here by dividing by on and we can put this guy on the bomb here by divine divided by that function on that will give us a function of X times by the X plus a function of why times d y equals there, Uh, which is in the form off a separable best defensive equation. Okay, Is it linear? It's definitely not linear because this guy has some know mania functions off. Why is exact? Well, if it were exact, then we would need the wide derivative of this to equal the extra sieve off this. But clearly the wide derivative off this is gonna be a function of why the extras him of this It's gonna be a function of X, so therefore they kind of evil, so it cannot be exact function