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seen Nov 18 at 14:38

Oct
16
revised Elementary Question about limits
corrected tex
Oct
16
comment Elementary Question about limits
Such a mess? Is not a mess. The most you have to use the chain rule once!
Oct
16
suggested suggested edit on Elementary Question about limits
Oct
16
comment shock waves characteristics
Why don't you take a look at Witham's Linear and Nonlinear Waves?
Oct
16
revised A differential equation of Buckling Rod.
added tags
Oct
16
suggested suggested edit on A differential equation of Buckling Rod.
Oct
16
revised A differential equation of Buckling Rod.
added 1 characters in body
Oct
16
answered A differential equation of Buckling Rod.
Oct
15
revised Special Differential Equation
added 1342 characters in body
Oct
15
comment Special Differential Equation
@drN There is a known technique to transform the ode $$w'' + f(z) w'+ g(z) w= 0$$ to the more qualitative $$ y'' + q(z) y = 0$$ using $$w = y e^{-\frac{1}{2}\int f(z) dz}$$ For a sound reference, see Olver's Asymptotics and Special Functions (§7.1.1)
Oct
15
comment Special Differential Equation
@PeterTamaroff I believe the sign on the last two equations is wrong. Shouldn't it be $+F(u)$?
Oct
14
revised Special Differential Equation (Continued)
texified it, added link
Oct
14
comment Special Differential Equation (Continued)
The first suggestion would be to write it in a easy to look form, i.e. $$ \frac{d^2 y}{d x^2} + \frac{1}{x} \frac{d y}{d x} + \left(-\frac{a}{x^2} - \frac{c}{x} + bxe^{-x^2/p^2}-de^{-x^2/p^2}\right) y = 0$$
Oct
14
comment Special Differential Equation (Continued)
As before, what's the domain of $x$?
Oct
14
suggested suggested edit on Special Differential Equation (Continued)
Oct
14
comment Special Differential Equation
What is the domain of your problem?
Oct
14
comment Can someone show me a proof of the general solution for 2nd order homogenous linear differential equations?
@IanMateus But you did! When you solved the second first order ODE (the one for $v$), you took the integrating factor $e^{u x}$ and implicitly assumed that $u \neq v$. If $u = v$ then $$ \frac{d}{dx}\left(e^{-u x} y\right) = C$$ and voila!
Oct
14
comment Can someone show me a proof of the general solution for 2nd order homogenous linear differential equations?
@IanMateus You should complement the answer with the one root case (it's right around the corner). Very nice use of factorization. (+1)
Oct
12
answered Special Differential Equation
Oct
12
revised Show $\left\lvert\sum_{k=-n}^n \frac{\sin k t }{k}\right\rvert \le \pi + 2$ for all $n$ and $t$, $t \in [0,2\pi]$
clarified the formula