# Tagged Questions

Questions on (ordinary) differential equations. For questions specifically concerning partial differential equations, use the (pde) tag.

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### Can Fredholm integral equation of the first type be represented as a differential equation?

Can Fredholm integral equation of the first type be represented as a differential equation? In other words, given a Fredholm integral equation of the second type does there exist a differential ...
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### Efficiently solving a large, sparse linear system $M(s)ab(s)=c(s)$ (determined by smooth functions) over some range of $s$

I'm looking at a differential equation on the edges of a graph (the application is neuroscience), and the Laplace transform of the solution on most of the edges has a general solution more-or-less of ...
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### Possibly new solution to equal-mass three-body problem; refinement required

(Since I didn't know which authorities to contact, I thought I'd post this here.) While messing around in this Wolfram Demonstrations applet, I found a suspicious pattern, in which I could see ...
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### Show that a solution of the complex ODE, with analytic coefficients, is itself analytic

Given the complex second order linear ODE $W''(z) + p(z) W'(z) + q(z) W(z) = 0$ show that the solution $W$ is analytic under assumption that $p$ and $q$ are so too. I thought that if a solution ...
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### An analytic method to prove a specific curve is closed

In my study of Hamiltonian dynamics I have come across a Hamiltonian dynamic system with a solution curve I know to be closed via computer and via intuition but I require a rigorous way to prove this, ...
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### Dissipation term in wave equation

If we're given a string with mass density $\rho$ in units $\frac{M}{L^3}$ with constant cross-section $A$, tension $T$ in units $\frac{F}{L^2}$, and whose length is $L$; and then we assume that the ...
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### WKB problem with 4 turning points?

I was recently given a problem that asked to find the solvability conditions for $$\epsilon^2y''=(W(x)-E)y;\quad y\rightarrow0\text{ as }|x|\rightarrow0$$ where $W$ was some piecewise linear, $`W"$-...
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### Find the paths along which water will run down the sides of a smooth football.

A smooth football having the shape of a prolate spheroid 12 inches long and 6 inches thick is lying outdoors in a rainstorm. Find the paths along which water will run down its sides. (Differential ...