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geduiwelh
2021-09-17
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tabuordg

Answered 2021-09-18
Author has **99** answers

Step 1

Given that,

Now , we know laplace transformation of

Also we know , property of unilafenal Linear transformation is

F(w)dw : where F(w) is the Laplace transformation of f(t)

Now , Laplace transformation of

Now , linear transformation of

But for

Now ,

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Solve the following IVP using Laplace Transform

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Find:

asked 2022-03-17

As part of trying to solve a differential equation using Laplace transforms, I have the fraction $\frac{-10s}{({s}^{2}+2)({s}^{2}+1)}$ which I am trying to perform partial fraction decomposition on so that I can do a inverse Laplace transform. When I try to work out this fraction, I get that $-10=0(A+B)$ since $s}^{1$ does not show up in the fraction. How does partial fraction decomposition work for a fraction like this?

asked 2021-02-02

Solve the following differential equations using the Laplace transform and the unit step function

$y"+4y=g(t)$

$y(0)=-1$

${y}^{\prime}(0)=0,\text{where}g(t)=\{\begin{array}{ll}t& ,t\le 2\\ 5& ,t2\end{array}$

$y"-y=g(t)$

$y(0)=1$

${y}^{\prime}(0)=2,\text{where}g(t)=\{\begin{array}{ll}1& ,t\le 3\\ t& ,t3\end{array}$

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The laplace transform for ramp function with a time delay can be expressed as follows

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Take the Inverse Laplace Transform of the function.

$F\left(s\right)=\frac{1}{s({s}^{2}+2s+2)}$

asked 2021-09-14

Find f(t).