What is inverse Laplace of following function?

$$F(s)={L}^{-1}(\frac{\Gamma (-\frac{s}{a}+b+\frac{1}{4})}{\Gamma (\frac{1}{4}-\frac{s}{a})})$$

$$F(s)={L}^{-1}(\frac{\Gamma (-\frac{s}{a}+b+\frac{1}{4})}{\Gamma (\frac{1}{4}-\frac{s}{a})})$$

manudyent7
2022-09-17
Answered

What is inverse Laplace of following function?

$$F(s)={L}^{-1}(\frac{\Gamma (-\frac{s}{a}+b+\frac{1}{4})}{\Gamma (\frac{1}{4}-\frac{s}{a})})$$

$$F(s)={L}^{-1}(\frac{\Gamma (-\frac{s}{a}+b+\frac{1}{4})}{\Gamma (\frac{1}{4}-\frac{s}{a})})$$

You can still ask an expert for help

asked 2021-09-08

Find inverse Laplace transform

$F\left(s\right)=\frac{10}{{s}^{3}+4{s}^{2}+9s+10}$

asked 2021-02-04

Find the inverse Laplace transforms of the functions given. Accurately sketch the time functions.

a)$F(s)=\frac{3{e}^{-2s}}{s(s+3)}$

b)$F(s)=\frac{{e}^{-2s}}{s(s+1)}$

c)$F(s)=\frac{{e}^{-2s}-{e}^{-3s}}{2}$

a)

b)

c)

asked 2022-01-06

asked 2021-02-26

How many poles does the Laplace Transform of a square wave have?

a) 0

b) 1

c) 2

d) Infinitely Manhy

a) 0

b) 1

c) 2

d) Infinitely Manhy

asked 2021-09-05

Find $L\left[\frac{{e}^{-3t}-\mathrm{cos}2t}{t}\right]$

asked 2022-07-17

Using Laplace transforms calculate the solution of the ordinary differential equation $\frac{{d}^{2}y}{d{t}^{2}}-2\frac{dy}{dt}+y={e}^{-t}$, subject to the initial conditions y(0)=0 and $\frac{dy}{dt}(0)=1$. Select the correct answer from the following list.

$a)y(t)=\frac{3t{e}^{t}}{2}+\frac{{e}^{-t}}{4}-\frac{{e}^{t}}{4}\phantom{\rule{0ex}{0ex}}b)y(t)=t{e}^{t}+\frac{{t}^{2}{e}^{t}}{2}\phantom{\rule{0ex}{0ex}}c)y(t)=\frac{t{e}^{-t}}{2}-\frac{{e}^{-t}}{4}+\frac{{e}^{t}}{4}\phantom{\rule{0ex}{0ex}}d)y(t)=t{e}^{-t}+\frac{{t}^{2}{e}^{-t}}{2}\phantom{\rule{0ex}{0ex}}e)y(t)=\frac{t{e}^{-t}}{2}-\frac{{e}^{-t}}{2}+\frac{{e}^{t}}{2}$

$a)y(t)=\frac{3t{e}^{t}}{2}+\frac{{e}^{-t}}{4}-\frac{{e}^{t}}{4}\phantom{\rule{0ex}{0ex}}b)y(t)=t{e}^{t}+\frac{{t}^{2}{e}^{t}}{2}\phantom{\rule{0ex}{0ex}}c)y(t)=\frac{t{e}^{-t}}{2}-\frac{{e}^{-t}}{4}+\frac{{e}^{t}}{4}\phantom{\rule{0ex}{0ex}}d)y(t)=t{e}^{-t}+\frac{{t}^{2}{e}^{-t}}{2}\phantom{\rule{0ex}{0ex}}e)y(t)=\frac{t{e}^{-t}}{2}-\frac{{e}^{-t}}{2}+\frac{{e}^{t}}{2}$

asked 2021-12-08

Show that

$\int}_{0}^{\mathrm{\infty}}\frac{\mathrm{sin}\left(t\right)}{t}dt=\frac{\pi}{2$

by using Laplace Transform method. I know that

$L\left\{\mathrm{sin}\left(t\right)\right\}={\int}_{0}^{\mathrm{\infty}}{e}^{-st}\mathrm{sin}\left(t\right)dt=\frac{1}{{s}^{2}+1}$

by using Laplace Transform method. I know that