Learn Laplace Transform Equations with Plainmath

Recent questions in Laplace transform
trumansoftjf0 2022-11-11

Find the inverse Laplace transform of the following:$F\left(s\right)=\frac{2s+1}{{s}^{2}-2s+2}.$The answer is $f\left(t\right)=2{e}^{t}\mathrm{cos}t+3{e}^{t}\mathrm{sin}t$Obviously once you have the decomposed fraction the remainder of the problem is simple but I can't seem to get to that point. Could someone please lay out the steps to decompose F(s)?

perlejatyh8 2022-11-11

Evaluating the inverse laplace transform of $X\left(s\right)=\frac{2\cdot {a}^{4}\cdot s}{{s}^{4}+4\cdot {a}^{4}}$

nyle2k8431 2022-11-11

Calculate $\mathcal{L}\left\{\mathrm{arctan}\left(t\right)\right\}=\frac{F\left(s\right)}{s}$Final value theorem:Is it correct?

Yaretzi Mcconnell 2022-11-11

How to solve the following integral:$I={\int }_{0}^{\mathrm{\infty }}\mathrm{cos}\left(t\mathrm{l}\mathrm{o}\mathrm{g}\left(x\right)\right)\phantom{\rule{thinmathspace}{0ex}}{\mathrm{e}}^{-ax}\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}x,$where t and a are real.

Humberto Campbell 2022-11-11

If $y\left(t\right)={\int }_{0}^{t}f\left(t\right)dt$ & the Laplace transform of f(t) is $\mathcal{L}\left\{f\left(t\right)\right\}={\int }_{0}^{\mathrm{\infty }}{e}^{-st}f\left(t\right)dt$,then prove that $\mathcal{L}\left\{y\left(t\right)\right\}=\left(1/s\right)\mathcal{L}\left\{f\left(t\right)\right\}$

Kailyn Hamilton 2022-11-11

Show using Laplace Transform that:The right hand side seems like it has something to do with the gamma function. Help with it please!

Josie Kennedy 2022-11-10

Solve by Laplace Transforms.How to find this ${\mathcal{L}}^{-1}$ $\left(\frac{\frac{5s}{4}+\frac{13}{4}}{{s}^{2}+5s+8}\right)$

Nola Aguilar 2022-11-10

Show that${\mathcal{L}}^{-1}\left[\frac{f\left(s\right)}{{s}^{2}}\right]={\int }_{0}^{t}{\int }_{0}^{x}F\left(x\right)dxdy.$I tried using the formula${\mathcal{L}}^{-1}\left[\frac{f\left(s\right)}{s}\right]={\int }_{0}^{t}F\left(x\right)dx.$

unabuenanuevasld 2022-11-10

Why is the inverse Laplace Transform of$\frac{\mathrm{sinh}\left(x\sqrt{s}\right)}{s\cdot \mathrm{sinh}\sqrt{s}}$equal to$x+\frac{2}{\pi }\sum _{n=1}^{\mathrm{\infty }}\frac{\left(-1{\right)}^{n}}{n}{e}^{-\left(n\pi {\right)}^{2}t}\mathrm{sin}n\pi x?$

Layton Park 2022-11-10

Use Laplace Transform to solve the following IVP:${y}^{″}+2{y}^{\prime }+5y={e}^{-t}\mathrm{sin}\left(2t\right)$ where $y\left(0\right)=2,{y}^{\prime }\left(0\right)=-1$

klesstilne1 2022-11-10

$F\left(S\right)=\frac{-S+11}{{S}^{2}-2S-3}$ How do I find f(t)? What is a good strategy for attacking these types of problems?

Josie Kennedy 2022-11-09

How can we find the inverse Laplace transform of the function $H\left(s\right)=\frac{8}{{s}^{4}+4}?$

Jenny Roberson 2022-11-09

How can I find the Inverse Laplace Transform of : ${\left(\frac{1-{s}^{1/2}}{{s}^{2}}\right)}^{2}$

linnibell17591 2022-11-09

How to solve this Laplace transform? $f\left(t\right)={e}^{-2t}{\mathrm{cos}}^{2}3t-3{t}^{2}{e}^{3t}$The answer is$\frac{1}{2\left(s+2\right)}+\frac{1}{2}\frac{s+2}{{s}^{2}+4s+40}-\frac{6}{\left(s-3{\right)}^{3}}.$How can this be solved?

fabler107 2022-11-08

Evaluate:I try it with laplace transfrom, but I cant find a result

Rosemary Chase 2022-11-08

Finding the inverse Laplace of this function $\frac{1}{{\left({s}^{2}+1\right)}^{2}}$

Humberto Campbell 2022-11-08

Find the Laplace transform of $g\left(t\right)=1+co{s}^{2}\left(2t\right)$ by direct integrationI'm having trouble finding out how to directly integrate the function f(t) because of the ${\mathrm{cos}}^{2}\left(2t\right)$ term. I understand that ${\mathrm{cos}}^{2}\left(2t\right)=\frac{1}{2}+\frac{1}{2}\mathrm{cos}\left(4t\right)$ but I don't understand how this simplifies the problem so that${\int }_{0}^{\mathrm{\infty }}{e}^{-st}+{\int }_{0}^{\mathrm{\infty }}{e}^{-st}\left(\frac{1}{2}+\frac{1}{2}\mathrm{cos}\left(4t\right)\right)$Is an easier integral to solve.

Kayley Dickson 2022-11-08