Here's the question you clicked on:
RolyPoly
\[\int \frac{dx}{lnx}\]
Do you know how to use integration by parts?
Integration by parts doesn't look nice..
\[\int \frac{dx}{lnx} = \frac{x}{lnx} - \int x d(\frac{1}{lnx})\]If that's what you meant...
u=lnx; x=e^u du=dx/x x du = dx \[\int \frac{1}{u}e^u~du\] maybe?
http://www.wolframalpha.com/input/?i=integrate+1%2Flnx you sure you got it right?
\[\int \frac{dx}{lnx}\]\[=\int \frac{x}{xlnx}dx\]\[=\int \frac{x}{lnx}d(lnx)\]\[=\int \frac{e^{lnx}}{lnx}d(lnx) \]\[=\int \frac{e^u}{u}du\]\[=\int \frac{1}{u}d(e^u)\].... The original question is \[y' = \frac{1}{y^2lnx}\]\[y^2 dy = \frac{dx}{lnx}\]I supposed integrating both sides can give me the answer :/
Perhaps I'm in the wrong direction?!
it looks like any solution will have to run into a logramathic integral
What technique(s) is(are) required to solve this equation?
ones that i havent run into yet :/
you can try to develop a series poly for it, and see what that would bring you
:O I haven't learnt expanding the function!
what methods have you learnt?
separable, integrating factors, exact question, undetermined coefficients, variation of parameters, homogeneous equation... Btw, I just ran around and grabbed the exercise, I think it's not in my textbook :/ http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/readings/notes_exe/MIT18_03S10_1ex.pdf 1A-3a
y^2 y' = 0 when y'=0 or y^2=0; given y1=0 and y2=C not sure of a wronskian would be useful here or not
Actually, how does Wronskian work. I just know it can determine the linear dependency.. Then, nothing :/
the wronskian is the short version of the undetermined coeffs
Wx W Wy f1 0 f2 f'1 g f'2 then its similar to the cross product W = f1f'2 - f'1f2 Wx = -g f2 Wy = f1 g and you integrate Wx/W and Wy/W
yeah, i dont see it being useful here tho
It...somehow... reminds me of Cramer's :/
it is, since the cramer is what you do at the end of the undetermined coeffs
Ahhhh.... Thanks for teaching something new though!!!
*teaching me something
yep, but as far as a solution to this goes; i got no idea. The wolf says we need a logartithmic integral which leads me to believe that this might be workable with a power series solution; but i dont think i can think thru it this late
Never mind, perhaps i should ask my teacher after the lesson today. I have to go for lesson now. Once again, thanks for your help!!
Sorry for the very late reply. I asked my teacher some days ago and he said I wouldn't know how to do it. Even for some graduate student, they didn't know that too. And he didn't teach me how to do the integration.... Thanks for your time helping me out!!