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### Numerically solve the initial value problem for the 1-D wave equation

I want to solve the standard 1-dimensional wave equation $y_{xx}=y_{tt}$ using NDSolve (for $y(x,t)$) with the following conditions: ...
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### Possible bug with FourierTransform linearity

Each component is easily transformed but the sum is not: FourierTransform[f''[x], x, k] FourierTransform[f'[x], x, k] ...
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### Solve PDE with DiracDelta function

This question is related to Analytic solution of dynamic Euler–Bernoulli beam equation with compatibility condition. I think it is more appropriate to open another question on this topic. In the ...
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### Bilateral Laplace Transform

I am trying to solve a linear ODE for a Kolmogorov forward equation to get a stationary distribution of a random variable. The easiest approach may be to transform the ODE with a two-sided Laplace ...
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### Obtaining the Fourier transform of an operator

We know that if we have a function $f(x)$, and we call $g(\omega)$ its Fourier transform, then the Fourier transform of $x f(x)$ is $$\imath \frac{\mathrm{d} g(\omega))}{\mathrm{d}\omega}$$ and ...
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### How to make an organised investigation of branch cuts from a solution to a differential equation

I am attempting to solve two differential equations. The solution gives equations that have branch cuts. I need to choose appropriate branch cuts for my boundary conditions. How do I find the correct ...
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### Solving the heat equation on the semi-infinite rod

Cross posted in scicomp.SE. I want to test the solution which is given below is right by Mathematica. Please look the post in mathstackexhange or Please look below. Question: Solve the ...
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### For Fourier Transform with $x(t)$, how to obtain result in terms of $X(f)$?

I have a function $x(t)$ and I denoted its Fourier transformation as $X(f)$. I want to get the Fourier transformation of $x(t)\mathrm e^{2\mathrm i \pi f_0 t}$, and I know the result is \$ X(f-...