# Tagged Questions

The Laplace transform is a widely used integral transform (transformation of functions by integrals), similar to the Fourier transform.

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### Solving ODE using Laplace transformation without table of transform

Solve $$y'' + 4y' -5y = 2xe^{-3x}$$ using the Laplace transform method. For the the Laplace transform of the ODE you must do the integration (do not use table). Table can be only used when computing ...
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### Laplace of a function raised to a power

For example: $y' = y + y^2$ The Laplace of the first two terms is $s(F(s)-f(0))$ and $F(s)$. But what is the Laplace of $y^2$?
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### Differential equations using Laplace transforms

By using Laplace transforms find $x(t)$ from the coupled differential equations$$\frac{dx}{dt} = -kx+gy+E,$$$$\frac{dy}{dt} = -ky-gx,$$for some functions $x(t),$ and $y(t)$, where $E, k, g$ are real. ...
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### Laplace transform of a convolution-like function

Is there a way to calculate the Laplace transform of the following function? $$\sum_{k=1}^{+\infty}f(t-(g(t)-\theta_k))h(g(t)-\theta_k), \qquad t>0.$$ Thanks in advance.
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### Consider the equation $y'' + 4y = f(t), y(0) = 1, y'(0) = 0$. Use the Laplace Transform to compute the Green’s function for this equation.

Consider the equation $y'' + 4y = f(t), y(0) = 1, y'(0) = 0$. Use the Laplace Transform to compute the Green’s function for this equation. $y'' + 4y = f(t) \rightarrow L\{y'' + 4y = f(t)\}=L\{f(t)\}$...
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### Laplace transform problem [closed]

This is the problem. I know ℒ (t^n) = ℒ (t^n-1) x n/s, which should give us -2/sqrt(s). That's as far as I've come and I don't get the hint either. Where does the pi even come from?
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### Cross-correlation, Fourier transform and Laplace transform: measure of how much signal are alike?

I'm studying electrical engineering and use correlation, Fourier transform and Laplace transform a lot. I know how and when to use them, however, the interpretation I've seen in the lectures still ...
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### Circuit Analysis problem (find the problem)

In this question, I know that $\text{C},\text{R},\text{T},\text{A}\in\mathbb{R}^+$ I've this circuit (the bottom of the resitor is connected to earth ($0$)): When I use Laplace transform I can find ...
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### Expressing the Weierstrass transform in terms of the unilateral Laplace transform

I was looking for a way to express the Weiestrass transform of $f(t)$, $$\mathcal{W}\{f(t)\}(s)=\frac{1}{\sqrt{4\pi}}\int_{-\infty}^{\infty}f(t)\exp\left(-\frac{(s-t)^2}{4}\right)dt$$ in terms of the ...
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### Laplace transform ODE

Use laplace transform to solve the ODE $y''(t)+4y(t)=4u(\pi-t)cos(t)$,,,,,,, $y(0)=y'(0)=0$ u is the unit step function (heaviside function) I use: $u(\pi-t)=1-u(t-pi)$ By inserting this and ...
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I'm studying circuit analysis. I've to solve this inverse Laplace transform to see the response: $$\mathcal{L}_{s}^{-1}\left[\frac{r}{r+\frac{1}{cs}}\cdot\frac{k\tanh\left(\frac{as}{2}\right)}{s}\... 1answer 28 views ### Using laplace trasnform find the convulation of (f*g)(t). let \;f(t)=\sin (3t) and g(t)=e^{-2t} Using laplace trasnform find the convulation of (f*g)(t). convulation theorem: h(t)=(f*g)(t)= \int ^t_0 f(u) g(t-u) du L(sin (3t)=\frac{3}{s^2+9}\\ L(e^... 1answer 25 views ### Inverse Laplace of an exponential function \exp{\{-x\sqrt{(s+h)/k}\}} I am having difficulty to figure out to use a Laplace Transform Table formula to verify a particular case. The inverse Laplace transform of$$L^{-1}\bigg[\exp{\bigg\{-x\sqrt{(s+h)/k}\bigg\}}\bigg]$$... 0answers 20 views ### The integral \int_{o}^{\infty} e^{-3t} cos(4(t-5))u(t-5) dt using laplace transform$$\int_{o}^{\infty} e^{-3t} cos(4(t-5))u(t-5) dt I need to find the laplace transform. Do i consider it as a convolution integral or as f(t)/t and work accordingly. Thank you. Edit: It turns out ...
Solving $y''+4y=g(t)$, $y(0)=3$, $y'(0)=-1$ using Laplace Transforms. I get $Y(s)=\frac{G(s)}{s^{2}+4}+\frac{3s}{s^{2}+4}-\frac{1}{s^2+4}$ Then using Inverse Laplace Transforms, I am not sure of my ...
i want to find the transfer function of a differential equation (given below) $\ddot\theta = a [ ([b\times Xin] - bk\dot\theta) - \ddot\theta] - c\phi$ (where $\phi$ and $\theta$ are time ...