Obtain the Laplace Transform of Lleft{e^{-2x}+4e^{-3x}right}

Laplace transform
asked 2021-03-18
Obtain the Laplace Transform of \(L\left\{e^{-2x}+4e^{-3x}\right\}\)

Answers (1)

Step 1
Laplace Transform: The Laplace transform provides an effective tool or way of solving initial-value problems for linear differential equations with constant coefficients. The type of problem differs accordingly with the question.
Step 2
The formula for calculating Laplace transform of \(e^{ax}=\frac{1}{(s-a)}\)
According to the question: \(L(e^{-2x} +4e^{-3x})\) we can separate the two terms
\(=\frac{(5s+11)}{(s^2+5s+6)}\) is the answer.

Relevant Questions

asked 2020-12-27
Obtain the Laplace Transform of
asked 2021-02-02
Obtain the Laplace Transform of
asked 2021-02-08
Use the Laplace transform table and the linearity of the Laplace transform to determine the following transform.
asked 2020-12-25
which of the laplace transform is
\(1.)\ L\left\{t-e^{-3t}\right\}=\frac{1}{s^{2}}+\frac{1}{s-3}\)
\(2.)\ L\left\{t-e^{-3t}\right\}=\frac{1}{s^{2}}-\frac{1}{s-3}\)
\(3.)\ L\left\{t-e^{-3t}\right\}=\frac{1}{s^{2}}+\frac{1}{s+3}\)
\(4.)\ L\left\{t-e^{-3t}\right\}=\frac{1}{s^{2}}-\frac{1}{s+3}\)
asked 2021-02-14
\(y'(0)=5\) First , using Y for the Laplace transform of y(t), i.e., \(Y=L\left\{y(t)\right\}\) find the equation you get by taking the Laplace transform of the differential equation
asked 2020-11-02
Find the Laplace transform \(L\left\{u_3(t)(t^2-5t+6)\right\}\)
\(a) F(s)=e^{-3s}\left(\frac{2}{s^4}-\frac{5}{s^3}+\frac{6}{s^2}\right)\)
\(b) F(s)=e^{-3s}\left(\frac{2}{s^3}-\frac{5}{s^2}+\frac{6}{s}\right)\)
\(c) F(s)=e^{-3s}\frac{2+s}{s^4}\)
\(d) F(s)=e^{-3s}\frac{2+s}{s^3}\)
\(e) F(s)=e^{-3s}\frac{2-11s+30s^2}{s^3}\)
asked 2020-11-29
Find the Laplace transform of \(\displaystyle f{{\left({t}\right)}}={t}{e}^{{-{t}}} \sin{{\left({2}{t}\right)}}\)
Then you obtain \(\displaystyle{F}{\left({s}\right)}=\frac{{{4}{s}+{a}}}{{\left({\left({s}+{1}\right)}^{2}+{4}\right)}^{2}}\)
Please type in a = ?
asked 2021-02-09
In an integro-differential equation, the unknown dependent variable y appears within an integral, and its derivative \(\frac{dy}{dt}\) also appears. Consider the following initial value problem, defined for t > 0:
a) Use convolution and Laplace transforms to find the Laplace transform of the solution.
b) Obtain the solution y(t).
y(t) - ?
asked 2021-01-06
Use laplace transform to solve the given system
\(a) \frac{dx}{dt} -2x- \frac{dx}{dt}-y =6e^{3t}\)
\(2\left(\frac{dx}{dt}\right)-3x+\frac{dx}{dt}-3y=6e^{3t} x(0)=3 y(0)=0\)
asked 2021-02-08
Use the Laplace transform to solve the following initial value problem:
a)take Laplace transform of both sides of the given differntial equation to create corresponding algebraic equation and then solve for \(L\left\{y(t)\right\}\) b) Express the solution \(y(t)\) in terms of a convolution integral