Jaylen Dudley
2022-09-16
Answered

Can the Inverse Finding the Laplace transform of $\frac{2s+1}{s(s+1)(s+2)}$ without using partial fractions?

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asked 2022-01-01

asked 2022-09-13

Identify the function f(t) that has the following Laplace transform,

$$\stackrel{~}{f}(s)={\int}_{0}^{\mathrm{\infty}}f(t){e}^{-st}dt={\left(\frac{1+\alpha s}{1+\alpha (s-{s}_{0})}\right)}^{p}$$

where $\alpha ,{s}_{0},p$ are positive parameters. Any suggestions about how to approach this problem?

$$\stackrel{~}{f}(s)={\int}_{0}^{\mathrm{\infty}}f(t){e}^{-st}dt={\left(\frac{1+\alpha s}{1+\alpha (s-{s}_{0})}\right)}^{p}$$

where $\alpha ,{s}_{0},p$ are positive parameters. Any suggestions about how to approach this problem?

asked 2021-01-27

Please solve the 2nd order differential equation by (PLEASE FOLLOW GIVEN METHOD) LAPLACE TRANSFORMATION

ALSO, USE PARTIAL FRACTION WHEN YOU ARRIVE

Problem 2 Solve the differential equation

and

asked 2021-12-31

asked 2021-02-25

Solve no.4 inverse laplace

${L}^{-1}\{s\mathrm{ln}\left(\frac{s}{\sqrt{{s}^{2}+1}}\right)+{\mathrm{cot}}^{-1s}\}$

asked 2021-09-15

Consider the following initial value problem:

$y\prime \prime -4y\prime -45y=\mathrm{sin}\left(7t\right),y\left(0\right)=1,y\prime \left(0\right)=-4$

Using Y for the Laplace transform of y(t), i.e., Y=L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)=?

Using Y for the Laplace transform of y(t), i.e., Y=L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)=?

asked 2022-09-11

How to prove the following identity regarding Laplace transforms?

$$\mathcal{L}[{\int}_{0}^{x}f(x-t)g(t)\text{}dt]=F(p)G(p)$$

$$\mathcal{L}[{\int}_{0}^{x}f(x-t)g(t)\text{}dt]=F(p)G(p)$$