# Tagged Questions

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

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### Infinite Series $\sum_{n=1}^\infty\frac{x^{3n}}{(3n-1)!}$

How can we prove that? $$\sum_{n=1}^\infty\frac{x^{3n}}{(3n-1)!}=\frac{1}{3}e^{\frac{-x}{2}}x\left(e^{\frac{3x}{2}}-2\sin\left(\frac{\pi+3\sqrt{3}x}{6}\right)\right).$$ I think if we write the taylor ...
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### Solving a differential equation?

I'm trying to analyze the transient state of a RC circuit. My book gives me the following differential equation: $$\frac{d(v(t))}{dt} + av(t) = c$$ for some constants $a$ and $c$. The book thens ...
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### $dy/dx = y \sin x-2\sin x$, $y(0) = 0$ — Initial Value Problem

$$\frac{dy}{dx} = y\sin x-2\sin x, \quad y(0) = 0.$$ Initial Value Problem Hint says: Find an integrating factor
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### find an approximate solution, up to the order of epsilon

The question is to find an approximate solution, up to the order of epsilon of following problem. $$y'' + y+\epsilon y^3 = 0$$ $$y(0) = a$$ $$y'(0) = 0$$ I tried to solve the given problem using ...
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### What is the optimal path between $2$ fixed points around an invisible obstructing wall?

Every day you walk from point A to point B, which are $3$ miles apart. There is a $50$% chance each walk that there is an invisible wall somewhere strictly between the two points (never at A or B). ...
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### Is it mathematically valid to separate variables in a differential equation?

I read the following statement in a book on Calculus, as part of my mathematics course: Technically this separation of $\frac{dy}{dx}$ is not mathematically valid. However, the resulting ...