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### FourierTransform a differental-equations [duplicate]

I want to use the command FourierTransform to transform a differential equations from time - domain to complex frequency domain but it don't works. My code is ...
68 views

### How do I let Fourier Transform know that it is a linear operator? [duplicate]

I have the following issue with FourierTransform, Fourier transform doesn't seem to know it is a linear operator. ...
43 views

### Fourier transform of an equation [duplicate]

I have the following equation: $$m \frac{d^2 x}{dt^2} = -Kx - \alpha \frac{dx}{dt} + f(t)$$ Which I introduced into Mathematica as: ...
27 views

### How to solve differential equations using FourierTransform[]? [duplicate]

I want convert a linear differential equation into the Fourier domain and solve the differential equation. ...
1k views

### 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: ...
1k views

### 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 ...
3k views

### 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 ...
880 views

### 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 ...
361 views

### 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] ...
856 views

### 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 ...
139 views

### 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 ...
247 views

### How to implement the finiteness condition for a PDE?

I have a PDE $$u_t=u_{yy}+u_{zz}$$ subject to the following initial and boundary conditions $$u(y=0,z>0,t>0)=1,$$ $$u(y=0,z<0,t>0)=0,$$ $$u(y=10,z,t>0)=0,$$ u(y,z=\pm10,t)\,\, \...
130 views

### unknown cause of scaling factors in NDSolve solutions to a partial differential equation

I am trying to solve a coupled diffusion partial differential equation with a Gaussian profile at t = 0. I would like to see how the two functions, y and z, evolve in time and in one dimension. This ...
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### Difference between FourierTransform and LaplaceTransform [duplicate]

There is an equation for example： eqn=D[c[x, t], t] == d D[c[x, t], x, x]; When I make a LaplaceTransform of it: ...
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### Collect terms in Fourier Transform

I want to collect terms in x from a product of polynomials and Fourier transform. So I try following code: ...
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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-...