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Asked Nov 25, 2019
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use the Laplace transform to solve the initial value problem.
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use the Laplace transform to solve the initial value problem.

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1, 0t<1
у" — 5у' + 4у
У (0) — 3,
у'(0) — —5
-1, 1 t<2,
7.
0, t 2,
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1, 0t<1 у" — 5у' + 4у У (0) — 3, у'(0) — —5 -1, 1 t<2, 7. 0, t 2,

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Expert Answer

Step 1

To solve using Laplace transform, first take laplace transform and use the following functions to convert it into function of s.

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L{yY(s)-y(0) L{y=sY(s)-sy(0)- y'(0)

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Step 2

Take Laplace transformation on both side of the differential equation,

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L{y"-5y'+ 4y- L{S (1)} Liv-5L{v}+41{y}= fes)t dt (-1) e e e-1-(e-e -S e-2* -2e +1

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Step 3

Substitute the value of Laplace transfor...

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2e 1 'r(s)-sy(0)-y(0) - [sY (s)-y (0)]+ 4Y (s) =

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