3,208 reputation
2830
bio website
location Buenos Aires, Argentina
age 21
visits member for 3 years, 8 months
seen 8 hours ago

(my about me is currently blank)


Feb
29
comment How to solve $y'' = -\frac{k}{y^2}$, with $k > 0$?
I end up with $\int \frac{\mathrm{d}y}{\sqrt{\frac{2k}{y}+C}} = \int \mathrm{d}x$. According to WolframAlpha, the integral on the left hand side is quite complicated, and it seems impossible to solve for $y=y(x)$. Am I doing something wrong?
Feb
29
comment How to solve $y'' = -\frac{k}{y^2}$, with $k > 0$?
Well, I get $y' = \pm \sqrt{2k(\frac1{y}-\frac1{y(0)})}$ (I made it clearer in the title that the right hand side of the equation should be negative), but I don't know how to go from there.
Feb
29
revised How to solve $y'' = -\frac{k}{y^2}$, with $k > 0$?
edited title
Feb
28
comment How to solve $y'' = -\frac{k}{y^2}$, with $k > 0$?
@Henry: I know, but mathematically does it make any difference?
Feb
28
asked How to solve $y'' = -\frac{k}{y^2}$, with $k > 0$?
Feb
19
comment A basic question about integration
@Gingerjin: the limit when $x$ goes to $0$ is $\infty$, not $0$, so it doesn't make sense to define it as such. It would not be continuous.
Feb
19
comment A basic question about integration
$x^{-\frac1{2}}$ is not integrable in $[0, 1]$, because it's not defined at $x = 0$.
Feb
16
accepted Confused about characteristic equation of a linear ODE
Feb
16
comment Confused about characteristic equation of a linear ODE
I guess that makes sense. If I understand correctly the idea is that you want a real space of solutions so you try to find a base made out of real functions, right?
Feb
16
asked Confused about characteristic equation of a linear ODE
Feb
11
answered Where should the exponent be written in numbers with units of measurement?
Feb
6
accepted Am I doing this double integral right?
Feb
5
asked Am I doing this double integral right?
Feb
4
accepted How to justify this differential manipulation while integrating?
Jan
17
revised Trigonometrical functions
latexified
Jan
17
suggested suggested edit on Trigonometrical functions
Jan
8
revised Solving $\int\frac{\ln(1+e^x)}{e^x} \space dx$
Misdiagnosed the error
Jan
8
answered Solving $\int\frac{\ln(1+e^x)}{e^x} \space dx$
Jan
5
comment How to justify this differential manipulation while integrating?
@AlexE: I don't really remember why I did that, but I know that I did. The exercise was to find an expression for velocity in terms of position for an object thrown up from the Earth, taking into account that fact that gravity changes with height: the equation was $y'' = G \frac{m_E}{(y+R_E)^2}$, where $m_E$ is Earth's mass and $R_E$ is its radius.
Jan
5
accepted Taking the derivative of $\frac1{x} - \frac1{e^x-1}$ using the definition