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

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

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asked 2021-03-18

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

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asked 2021-02-02

Obtain the Laplace Transform of
\(L\left\{t^3-t^2+4t\right\}\)
\(L\left\{3e^{4t}-e^{-2t}\right\}\)

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asked 2021-02-08

Use the Laplace transform table and the linearity of the Laplace transform to determine the following transform.
\(L\left\{e^{3t}\sin(4t)-t^{4}+e^{t}\right\}\)

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asked 2020-12-25

\(L\left\{t-e^{-3t}\right\}\]
which of the laplace transform is
\(1.)\ L\left\{t-e^{-3t}\right\}=\frac{1}{s^{2}}+\frac{1}{s-3}\)
\(2.)\ L\left\{t-e^{-3t}\right\}=\frac{1}{s^{2}}-\frac{1}{s-3}\)
\(3.)\ L\left\{t-e^{-3t}\right\}=\frac{1}{s^{2}}+\frac{1}{s+3}\)
\(4.)\ L\left\{t-e^{-3t}\right\}=\frac{1}{s^{2}}-\frac{1}{s+3}\)

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asked 2021-02-14

\(y"-8y'+41y=0\)
\(y(0)=0\)
\(y'(0)=5\) 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

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asked 2020-11-02

Find the Laplace transform \(L\left\{u_3(t)(t^2-5t+6)\right\}\)
\(a) F(s)=e^{-3s}\left(\frac{2}{s^4}-\frac{5}{s^3}+\frac{6}{s^2}\right)\)
\(b) F(s)=e^{-3s}\left(\frac{2}{s^3}-\frac{5}{s^2}+\frac{6}{s}\right)\)
\(c) F(s)=e^{-3s}\frac{2+s}{s^4}\)
\(d) F(s)=e^{-3s}\frac{2+s}{s^3}\)
\(e) F(s)=e^{-3s}\frac{2-11s+30s^2}{s^3}\)

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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 = ?

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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:
\(\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{t}\right.}}}+{4}{\int_{{0}}^{{t}}}{y}{\left({t}-{w}\right)}{e}^{{-{4}{w}}}{d}{w}={3},{y}{\left({0}\right)}={0}\)
a) Use convolution and Laplace transforms to find the Laplace transform of the solution.
\({Y}{\left({s}\right)}={L}{\left\lbrace{y}{\left({t}\right)}\right)}{\rbrace}-?\)
b) Obtain the solution y(t).
y(t) - ?

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asked 2021-02-08

Use the Laplace transform to solve the following initial value problem:
\(2y"+4y'+17y=3\cos(2t)\)
\(y(0)=y'(0)=0\)
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

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asked 2020-12-29

Find the laplace transform of the following:
Change of Scale
\(\text{If } L\left\{f(t)\right\}=\frac{s^2-s+1}{(2s+1)^2(s-2)} \text{ , find } L\left\{f(2t)\right\}\)

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Answer 1

\(\text{step 1}\)
\(\text{laplace transform of }L\left\{e^{-2x}+4e^{-3x}\right\}\)
\(=\int_0^\infty e^{-sx}f(x)dx\)
\(=\int_0^\infty e^{-sx}(e^{-2x}+4e^{-3x})dx\)
\(\text{Step 2}\)
\(=\int_0^\infty (e^{-(s+2)x}+4e^{-(s+3)x})dx\)
\(=\left[\frac{e^{-(s+2)x}}{-(s+2)}+\frac{4e^{-(s+3)x}}{-(s+3)}\right]_0^\infty\)

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

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

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