How do I find the interval for solving this differential equation?

[karush]

View attachment 8690
doing #1

ok first I divided thru

$$y' + \frac{\ln{t}}{t-3}y=\frac{2t}{t-3}$$

but the $$\exp\int p(t) \, dt$$ step kinda baloated?

ok I see the denominator has $t-3$ so presume 3 is one of the interval ends
but why 0. ?

book answwer is

View attachment 8691

 

[HOI]

"Baloated"?

The reason for the restriction x> 0 is the "ln(x)" term.

 

[karush]

"Baloated"?

The reason for the restriction x> 0 is the "ln(x)" term.

you probably mean $ln{t}$

yeah how would this really work $e^{p}$
View attachment 8693

 

[HOI]

I am not sure what you are asking. Do you know what "$Li_2(x)$" is?

 

[topsquark]

yeah how would this really work $e^{p}$

But your problem statement said not to solve the equation. So why are you introducing the [math]e^p[/math] into your solution?

-Dan