/sci/ - Science & Math

Sorry I can't help you. I'm bad with math. 2N+2N looks 4N to me.

You mean dy/dx = e^y? Uhm... You could always separate variables
e^-y dy = 1 dx
Integrate both sides
-e^-y = x + C
e^-y = D - x
-y = ln(D-x)
y = -ln(D-x)

Checking we have
dy/dx = 1/(D-x)
but e^-ln(D-x) = 1/e^ln(D-x) = 1/(D-x)

The answer is yes, y = f(x) = 1/(D-x) works for every real constant D.

Maybe I'm understanding it wrong, but <span class="math">\int x^x dx[/spoiler] is not defined.

>>1847571
It's perfectly well-defined, although there may not be an elementary expression matching that function.

>>1847562
Derp, that should be
>y = f(x) = -ln(D-x) works for every real constant D

>>1847571
x^x is continuous, therefore, it is integrable. It probably can't be expressed in terms of elementary functions, though.

>>1847578
>>1847581
That's what I meant, thanks for clearing it up.

>>1847562
i'm trying to understand, all i don't get is what you mean by separate the variables and how you got from
dy/dx = e^y
to
e^-y dy = 1 dx

>>1847594
<div class="math"> \frac{dy}{dx} = e^y</div>
<div class="math"> e^{-y} \frac{dy}{dx} = 1</div>
<div class="math"> e^{-y} dy = dx</div>

>>1847594
Multiply both sides by e^-y dx.

>>1847606
>>1847602
ok yeah that was a stupid question haha. thank you so much!

>He thinks he can learn mathematics outside of a university!

>Aaahahahahahahahaha

>Laughing_attractive_university_students.jpg

>>1847606 Multiply both sides by dx

There are only 1 kinds of people!?

fuck that shit

>>1847652
Problem, officer?

>>1847666
1-forms are legit.

>>1847652
>implying you're not a physicist

>>1847732
Multiplying with differentials is like dividing by vectors. My physicist opinion.

>>1847736

>>1847736

wtf am I doing with the differential when I'm multiplying with it?

>>1847745
You're multiplying with it, obviously!

>>1847745
<div class="math">dx = 1 dx = e^{-y}\frac{dy}{dx}dx = e^{-y}\frac{\partial y}{\partial x}dx = e^{-y}dy</div>
Something like that.

For one-variable continuous functions you can deal with differentials as if they were normal numbers, i guess