differential equations help!! has anyone taken the class recently???? I really need help on these problems

Question

anonymous · Answer

$$xy'''-3y'+e^xy=x^2-1$$
$$y(-2)=1, y'(-2)=0, y''(-2)=2$$
the answer is (-infinity,0)

anonymous · Answer

In Problems 1–6, determine the largest interval (a,b) for
which Theorem 1 guarantees the existence of a unique
solution on (a,b) to the given initial value problem

anonymous · Answer

@Mertsj @phi @robtobey if you guys could help or mention someone that could it would be appreciated. im looking at the book now to see how it's done......

phi · Answer

what is Thm 1 ?

anonymous · Answer

http://prntscr.com/1hqnvh

anonymous · Answer

@phi there is theorem 1

anonymous · Answer

@oldrin.bataku

anonymous · Answer

@oldrin.bataku don't worry about it friend already got this one...just took about 2 hours for someone to finally help lol

anonymous · Answer

I want to know, ignore him,please tell me how to solve it.

anonymous · Answer

$$xy'''-3y'+e^xy=x^2-1$$Observe that theorem 1 considers IVPs in standard form, so divide thru by $x$:$$y'''-\frac3xy'+\frac{e^x}xy=\frac{x^2-1}x$$We're interested in intervals of continuity, and clearly our coefficient functions are all continuous on $(-\infty,0),(0,\infty)$ (because of the poles at $x=0$). We're interested in the largest interval of continuity containing the initial point used for our initial values, here $x_0=-2$, hence we pick $(-\infty,0)$.

anonymous · Answer

sorry @rperez36 I was eating. @looser66 see above

anonymous · Answer

then?

anonymous · Answer

@looser66 that's it :-p theorem 1 tells us that the IVP has a unique solution on any interval on which our coefficient functions are continuous and we picked the largest one that contains $-2$