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

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Rigorous separation of variables.

Let $I \subseteq \mathbb{R}$ denote an open, non-empty subinterval of the real line. We're given functions: $$f : I \rightarrow \mathbb{R}, \;\;g : \mathbb{R} \rightarrow \mathbb{R}.$$ Now suppose ...
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Separable ODE and singular solutions

In most introductory ODE textbooks we can find the following definition: A separable first-order ODE is the one of the form $$y'=g(x)h(y)$$ and if $h(y)\neq0$, then the general solution is found by ...
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Laplace's equation in Polar coordinate, an example?

Consider Laplace's equation in Polar coordinate $ \frac {1}{r} \frac {\partial} {\partial r} (r \frac {\partial u} {\partial r}) + \frac {1} {r^2} \frac {\partial^2 u} {\partial \theta^2}$ with ...