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Finding singular solution to a Lagrange equation
A differential equation of type
$$y = x\varphi \left( {y'} \right) + \psi \left( {y'} \right),$$
where φ (y' ) and ψ (y' ) are known functions differentiable on a certain interval, is called the ...
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Global existence of an ODE
To guarantee the existence of a global solution (you can't in general), you need to look at the forward dynamics $u'=f(u)$ and the reverse dynamics $u'=-f(u)$.
Let $f(u) = u-u^3$, note that $f(u) = 0 $...
- 174k
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Can we convert the following integral equation to a differential equation:$h(r)= \int_0^\infty\frac{f(x)}{e^{r x} + 1} dx$?
Alternatively, you can consider a little bit more general problem by introducing an auxiliary variable and defining the following function :
$$
g(r,s) := \int_0^\infty \frac{f(sx)}{e^{rx}+1} \,\mathrm{...
- 10.3k
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