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Step 5 We have found y in terms of Inverse Laplace transforms and the resulting transforms as follows. $y(t) = \frac{2}{125}\mathcal{L}^{-1}\left\{\frac{1}{s}\right\} + \frac{1}{25}\mathcal{L}^{-1}\left\{\frac{1}{s^2}\right\} - \frac{2}{125}\mathcal{L}^{-1}\left\{\frac{1}{s-5}\right\} + \frac{26}{25}\mathcal{L}^{-1}\left\{\frac{1}{(s-5)^2}\right\}$ $\mathcal{L}^{-1}\left\{\frac{1}{s}\right\} = 1$ $\mathcal{L}^{-1}\left\{\frac{1}{s^2}\right\} = t$ $\mathcal{L}^{-1}\left\{\frac{1}{s-5}\right\} = e^{5t}$ $\mathcal{L}^{-1}\left\{\frac{1}{(s-5)^2}\right\} = te^{5t}$ To finish, solve the given initial-value problem. $y = \frac{2}{125} + \frac{t}{25} - \frac{2}{125}e^{5t} + \frac{26}{25}te^{5t}$

Name: step 5 we have found y in terms of inverse laplace transforms and the resulting transforms as follows yt frac2125mathcall 1leftfrac1sright frac125mathcall 1leftfrac1s2right frac2125mathcall 02363
Uploaded: 2022-06-13T10:07:14-08:00
Duration: 2 min 46 s
Channel: Shaiju T
Description: step 5 we have found y in terms of inverse laplace transforms and the resulting transforms as follows yt frac2125mathcall 1leftfrac1sright frac125mathcall 1leftfrac1s2right frac2125mathcall 02363

          Step 5
We have found y in terms of Inverse Laplace transforms and the resulting transforms as follows.
$y(t) = \frac{2}{125}\mathcal{L}^{-1}\left\{\frac{1}{s}\right\} + \frac{1}{25}\mathcal{L}^{-1}\left\{\frac{1}{s^2}\right\} - \frac{2}{125}\mathcal{L}^{-1}\left\{\frac{1}{s-5}\right\} + \frac{26}{25}\mathcal{L}^{-1}\left\{\frac{1}{(s-5)^2}\right\}$
$\mathcal{L}^{-1}\left\{\frac{1}{s}\right\} = 1$
$\mathcal{L}^{-1}\left\{\frac{1}{s^2}\right\} = t$
$\mathcal{L}^{-1}\left\{\frac{1}{s-5}\right\} = e^{5t}$
$\mathcal{L}^{-1}\left\{\frac{1}{(s-5)^2}\right\} = te^{5t}$
To finish, solve the given initial-value problem.
$y = \frac{2}{125} + \frac{t}{25} - \frac{2}{125}e^{5t} + \frac{26}{25}te^{5t}$

$step 5 we have found y in terms of inverse laplace transforms and the resulting transforms as follows yt frac2125mathcall 1leftfrac1sright frac125mathcall 1leftfrac1s2right frac2125mathcall 02363$

Added by Joseph C.

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