# Tagged Questions

31 views

### Does an inverse Laplace transform for $\hat{F}(s)=e^{-is}$ exist? If not, why?

Does an inverse Laplace transform for $\hat{F}(s)=e^{-is}$ exist? If not, why? The Bromwich integral is not covered in my course so I can't use it. I'm hoping and guessing that the answer is simple! ...
12 views

51 views

### Elliptical Coordinates PDE, wave equation and separation of variables

I need some help with this problem. I know how to use the method of separation of variables and that the constant lambda should give you trig functions with solutions at some interval of pi, which ...
98 views

### Intuition behind convolution identity for Laplace transforms

Convolutions, relatively speaking, are fairly straightforward for simple systems (from an applied perspective), but I cannot, at all, find the intuition behind the Laplace identity for convolutions. ...
26 views

### Laplace transform of Differential Equation with a piecewise function

Hi I have this question and I am horribly stuck at one part and I cant seem to figure out if i did something wrong so any advice or help would be greatly apprecaited. Here is the question: ...
32 views

### Dirac Delta Function, Initial Value Problem

Hi I finished this IVP but I cant seem to get the right answer can someone give me some advice as to where I went wrong and point me in the right direction as to how to fix it. Here is the problem and ...
65 views

### Laplace transformation $y''+2y'+2y=3\sin x+\cos x$

Given$$y''+2y'+2y=3\sin x+\cos x$$ Transform to image region $$Y(s)(s^2+2s+2)=\frac{3}{s^2+1}+\frac{s}{s^2+1}-s-2$$ $$Y(s)((s^2+2s+1)+1)=\frac{3}{s^2+1}+\frac{s}{s^2+1}-s-2$$ ...
43 views

### Laplace transform of a differential equation

Given the Laplace transform \begin{align} \mathcal{L}\{g(r)\} = f(t) = \int_{0}^{\infty} e^{-tr} g(r) \ dr \end{align} can it be shown that the transform of the differential equation \begin{align} ...
60 views

### Solving an ODE using Laplace Transforms

$$y′′′′ + 2y′′ + y = \sin x$$ $$y(0) = y′(0) = y′′(0) = y′′′(0)= 0$$ After solving I got $y(s)=\dfrac1{(s^2 + 1)^3}$ for which I am unable to find the inverse Laplace transform. Please let me know ...
25 views

65 views

### Laplace Trouble to find solution

Trying to figure out how to use Laplace Transform to find $y(t)$: The problem is $$y''+4y'+4y=f(t)$$ where $f(t) = \cos(\omega t)$ if $0 < t < \pi$ and $f(t)=0$ if $t > \pi$? Initial ...
44 views

189 views

### $y''+2y'+5y=0$, initial value problem with Laplace transform?

here is the question: $${\rm y}''\left(t\right) + 2\,{\rm y}'\left(t\right) + 5\,{\rm y}\left(t\right) = 0; \qquad\qquad {\rm y}\left(0\right) = 2\,,\quad {\rm y}'\left(0\right) = -1.$$ ...
26 views

### Find Laplace Transform of the following function

How do I find the Laplace transform for the function: $f(t)=t, 0 \leq t \leq 1$ and $2-t, t \geq 1$ I tried looking up the process online, but it remains unclear to me. Thanks in advance!