# Tagged Questions

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

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### Constructing a function using the Fourier transform

Pick an integer $n\ge 5$ and let $f\in C_{C}^{\infty}(\mathbb{R}^{N})$. We want to use the Fourier transform to formally construct a function $u\in L^{\infty}(R^{n})$ that solves $\Delta^{2}u(x)=f(x)$...
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### Leading behaviour of DE at infinity

This is taken from the book of Bender and Orszag, problem 3.44. Find the leading behavior as $x\rightarrow+\infty$ of the differential equation: $x^3y'' - (2x^3 -x^2)y' +(x^3-x^2-1)y=0$ Explain ...
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### Is there a fiber bundle approach to nonlinear oscillations?

I've recently been learning about nonlinear oscillations, and I noticed a seemingly strong connection between how the equations of motion are solved/approximated, and fiber bundles (or vector bundles ...
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### Are there any symplectic integration techniques that are A-stable (work on stiff equations)?

The first and second Dahlquist Barriers show that (paraphrasing): Explicit multi-step methods cannot be A-stable and thus are not accurate for stiff equations. Implicit multi-step methods will only ...
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### Estimating limit cycle of ODE system

I'm looking at a system of ODEs: $$\dot{x} = -y - \epsilon^2 x + xy^2$$ $$\dot{y} = x -\epsilon^2 y - x^2$$ After plotting these in Matlab I can see there is a limit cycle very close to the origin ...
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### Is this a valid equivalence between the classes of Differential Equations?

Consider the general first order Linear Ordinary Differential Equation: $$\frac{dy}{dx} = A(x,y) = \frac{F(x,y)}{G(x,y)}$$ This equation is characteristic equation of the Partial Differential ...
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### Solving $2y'''(t)+3t\ y(t)=0$.
For a certain problem, I am trying to solve the ODE $$2y'''(t)+3t\ y(t)=0$$ I am pretty clueless what to do here, any hint would be appreciated. Thank you very much.