Recent content by bcyang

Homework Statement The problem occurred when solving x'' - \frac{1}{x^2} = 0 . You can think of this as if there is a mass in the origin (M) and a small particle (m << M) is being pulled by this mass. Daniel helped me to solve this diff. eq. and we are at Homework Equations...

Thank you, Daniel.

No, I don't know how to separate variables. Please help...

I guess no (though I learned it once upon a time). Sorry.

Oh, I see. Isn't it \frac{dx}{2\sqrt{C-1/x}} = dt

Thank you again. This is not how I should approach it, isn't it? x' = 2\sqrt{C-1/x}

Thanks a lot. So, I have \frac{1}{2}(x')^2 - \frac{1}{x} = C where C is a constant. I feel so hopeless. I still don't see how I can solve this:(

Perhaps \frac{d}{dt} (x')^2 = 2 x' x'' helps?

Sorry, Daniel. I guess it's been too long since I left college. My brain is all rusty:(

Perhaps a little more hint:) Thank you, Kurt.

Thanks. I was solving (which I thought is) a trivial diff eq. where there is some repeling force from an origin to an electron, say, at x. So, the diff eq. really boils down to x'' - 1/x^2 = 0 which I wonder if it even has a closed form solution. Thank you all in advance. Yang

Sorry. I should have put this into "diff eq."

Can anybody solve this problem? I don't think this is something that we see in an elementary diff eq textbook. Thank you in advance. Yang