# Tagged Questions

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

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### What is the Fourier Transform of this function $\frac{e^ \frac{1}{2}t(-w^2 +2 \sqrt{2 \pi} u \delta''(w)) }{ \sqrt{2 \pi}}$?

As the title says, what is the Inverse Fourier Transform of this function: $$\frac{e^ \frac{1}{2}t(-w^2 +2 \sqrt{2 \pi} u \delta''(w)) }{ \sqrt{2 \pi}}$$ The inverse should be taken with ...
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### How to solve $y'' + y = -2\sin(x)$?

I don't know how to find the particular solution of $$y'' + y = -2\sin(x)$$ I started with $$y'' + y = 0$$ to find the homogeneous form $$A\cos(x)+B\sin(x)$$ But now i am stuck.
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### Intuition on the necessity of the Lipschitz condition and a physical example of an ODE

The Picard-Lindelöf theorem states that the initial value problem $$y'(x) = F(x,y(x)), \ y(x_0) = y_0$$ will always have a unique solution on some closed interval containing $x_0$ assuming that the ...
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### How to tell if you have specified sufficient initial data for a differential equation?

I recently learnt that the following 'wave equation' is not well-posed $$\begin{cases} \partial_{tt}u=\partial_{xx} u, & (0,1)\times\mathbb R\\ u(t,0)=u(t,1)=0,&t\in [0,1] \end{cases}$$ ...
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### determine the indical equation for the following differential equation

$x^3y''+(\cos2x-1)y'+2xy=0$ One have to make the anstaz that $y= x^m \sum_{j=0}^{\infty}a_j x^j$ and I have been solving problems like this before, but for this one what really confuses me is what to ...
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### Differential form of surface integral equation

Considering a scalar field in a plane (pressure vs. location) $P({\rm r})$ where ${\rm r}=(x,y)$ then the following surface integral gives the surface deformation due to the pressure in the elastic ...
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