# Learn Laplace Transform Equations with Plainmath

Recent questions in Laplace transform
Eliza Shields 2023-04-01

## The Laplace transform of $u\left(t-2\right)$ is (a) $\frac{1}{s}+2$(b) $\frac{1}{s}-2$(c) ${e}^{2}\frac{s}{s}\left(d\right)\frac{{e}^{-2s}}{s}$??

Gianna Johnson 2023-04-01

## The Laplace transform of the product of two functions is the product of the Laplace transforms of each given function. True or False

inframundosa921 2023-03-21

## The Laplace transform of $t{e}^{t}$ is A. $\frac{s}{\left(s+1{\right)}^{2}}$ B. $\frac{1}{\left(s-1{\right)}^{2}}$ C. $\frac{s}{\left(s+1{\right)}^{2}}$ D. $\frac{s}{\left(s-1\right)}$

enrosca0fx 2023-01-03

## What is the Laplace transform of $t\mathrm{cos}t$ into the s domain?

klupko5HR 2022-11-25

## Find the inverse Laplace transform of $\frac{{s}^{2}-4s-4}{{s}^{4}+8{s}^{2}+16}$

phumzaRdY 2022-11-25

## How do i find the lapalace transorm of this intergral using the convolution theorem? ${\int }_{0}^{t}{e}^{-x}\mathrm{cos}x\phantom{\rule{thinmathspace}{0ex}}dx$

unecewelpGGi 2022-11-25

## What's the correct way to go about computing the Inverse Laplace transform of this?$\frac{-2s+1}{\left({s}^{2}+2s+5\right)}$I Completed the square on the bottom but what do you do now?$\frac{-2s+1}{\left(s+1{\right)}^{2}+4}$

hemotropS7A 2022-11-25

## How to find inverse Laplace transform of the following function?$X\left(s\right)=\frac{s}{{s}^{4}+1}$I tried to use the definition: $f\left(t\right)={\mathcal{L}}^{-1}\left\{F\left(s\right)\right\}=\frac{1}{2\pi i}\underset{T\to \mathrm{\infty }}{lim}{\int }_{\gamma -iT}^{\gamma +iT}{e}^{st}F\left(s\right)\phantom{\rule{thinmathspace}{0ex}}ds$or the partial fraction expansion but I have not achieved results.

Alberanteb4T 2022-11-24

## inverse laplace transform - with symbolic variables:$F\left(s\right)=\frac{2{s}^{2}+\left(a-6b\right)s+{a}^{2}-4ab}{\left({s}^{2}-{a}^{2}\right)\left(s-2b\right)}$My steps:$F\left(s\right)=\frac{2{s}^{2}+\left(a-6b\right)s+{a}^{2}-4ab}{\left(s+a\right)\left(s-a\right)\left(s-2b\right)}$$=\frac{A}{s+a}+\frac{B}{s-a}+\frac{C}{s-2b}+K$$K=0$$A=F\left(s\right)\ast \left(s+a\right)$

ingerentayQL 2022-11-24

## Laplace transform of $\left(3e{\right)}^{t}{\mathrm{sin}}^{2}t$

hemotropS7A 2022-11-24

## How to find the Direct Discrete Laplace Transform of $\left(\genfrac{}{}{0}{}{2n}{n}\right)$

Diana karen Sánchez González2022-11-22

## Transy''+ 5y'+ 6y = 0, y(0) = 1, y'(0) = 1

Leonard Dyer 2022-11-22

## Find Inverse Laplace Transform of $\frac{1}{\left({s}^{2}+1\right)\left({s}^{2}-2s+7\right)}.$

AimettiA8J 2022-11-22

## How to find the Laplace transform of $|\mathrm{sin}\left(t\right)|$?

undergoe8m 2022-11-21

## Show ${\int }_{s}^{\mathrm{\infty }}f\left(x\right)dx=\mathcal{L}\left\{\frac{F\left(t\right)}{t}\right\}$ given $f\left(x\right)={\int }_{0}^{\mathrm{\infty }}{e}^{-xt}F\left(t\right)dt$

Celeste Barajas 2022-11-21

## This integral sounds quite complex and I could not find an approximate equivalent. ${\int }_{0}^{+\mathrm{\infty }}x\mathrm{log}\left(1+{x}^{2}\right)\phantom{\rule{thinmathspace}{0ex}}{e}^{-Bx}\phantom{\rule{thinmathspace}{0ex}}dx$

figoveck38 2022-11-21

## Solve ${y}^{\prime }\left(t\right)=\mathrm{sin}\left(t\right)+{\int }_{0}^{t}y\left(x\right)\mathrm{cos}\left(t-x\right)dx$ by Laplace transformMy try:I applied Laplace transform on both sides of the equation.$sL\left\{y\left(t\right)\right\}=\frac{1}{{s}^{2}+1}+L\left\{cos\left(t\right)\ast y\left(t\right)\right\}\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}sL\left\{y\left(t\right)\right\}=\frac{1}{{s}^{2}+1}+L\left\{cos\left(t\right)\right\}×L\left\{y\left(t\right)\right\}$Now, I'm stuck on applying the inverse Laplace transform on (*) to find $y\left(t\right)$

Noe Cowan 2022-11-20