# Questions tagged [differential-equations]

Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.

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### A mistake in the solution of First-order system of linear differential equations [closed]

My solution: enter image description here enter image description here Wolfram Alpha solution: enter image description here Please help me to find a mistake.
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### Dynamical system described by coupled nonlinear differential equations

Suppose a dynamical system is described by two variables, $x$ and $y$, and they change over time according to the following two coupled nonlinear differential equations: \begin{equation} \begin{split} ...
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### Set of eigenvalues of the boundary problem

I'm looking for the results about the set of eigenvalues of boundary problem for differential equation \begin{equation} \bigl(p(x) u'(x; \lambda) \bigr)' + q(x) u(x; \lambda) = -\lambda w(x) u(x; \...
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### How to solve the integral equation $f(x)=\frac{\lambda\int_{x}^1 \sqrt{1+(f(t))^2}dt+c_1}{\int_{x}^1 \sqrt{1+(f(t))^2}dt+c_2}$?

Recently, I have asked a question about variational analysis (First moments of uniform distribution on a curve from (0,0) to (1,1) in two-space). Such the question can be addressed in some cases by ...
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### Continuous dependence on initial parameters of an ODE for non-Lipschitz functions?

For ODEs, the standard theorem of continuous dependence of initial parameters deals only with functions that are Lipschitz. Do there exist more general results holding for non-Lipschitz functions? If ...
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### Solution to differential equation $f^2(x) f''(x) = -x$ on [0,1]

I'd like to solve a differential equation $$f^2(x) f''(x)=-x$$ where $f(x)$ is defined on $[0,1]$ and has a boundary condition $f(0)=f(1)=0$. I somehow found out that the solution is fairly close ...
Consider the Lorenz system $$\dot{x}(t) = \sigma(y-x) \, ,$$ $$\dot{y}(t) = x(\rho-z) - y \, ,$$ $$\dot{z}(t) = xy-\beta z \, .$$ Usually one considers the parameters $\sigma, \rho,$ and $\beta$ to be ...