# Tagged Questions

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### Blowup of ODEs in the presence of local Lipschitzianity?

Pardon me if the question is trivial, but I am failing to decide it. Assume that we are given an ODE system $\dot{x} = f(x)$ with positive initial conditions $x(0)$ and know that $f$ is locally ...
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### Reducing size of ODE system by using symmetries: examples, references help request.

We know: A high order differential equation can be expressed as an ODE system. Knowledge of a symmetry allow one to reduce the order of a differential equation. So if we do $n$-order ODE ...
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### Vector field with bounded integral curves

I am thinking about smooth vector fields on some (open set of an) euclidean space $\mathbb{R}^n$. I know that the integral curves of a general vector field $X$ are not defined for every time \$t\in ...
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### Differential Equations without Analytical Solutions

In many talks, I have heard people say that the differential equation they are interested in has no analytical solution. Do they really mean that? That is: Can you prove a differential equation ...
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### Simple proof that non-linear DE's do no not satisfy superposition?

I'm wondering if there's a simple proof that solutions to non-linear differential equations do not satisfy the superposition principle? Some explicit examples would also be great. Cheers!
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### Examples of parameter dependent ODEs

I would like to have some examples of simple parameter dependent ODEs. I would like the solutions to have some physical meaning. I'll give one example so it clear what I am after: Example 1: The ...