5.5 Exercises Use the Laplace transform to solve each of the following systems of equations. 1. ⎩⎨⎧x′+y=3e2ty′+x=0x(0)=2y(0)=0 2. ⎩⎨⎧x′−2y=0y′+x−3y=2x(0)=3y(0)=0 3. ⎩⎨⎧x′−5x+2y=3e4ty′−4x+y=0x(0)=3y(0)=0 4. ⎩⎨⎧x′−2x−3y=0y′+x+2y=tx(0)=−1y(0)=0 5. ⎩⎨⎧x′−4x+2y=2ty′−8x+4y=1x(0)=3y(0)=5 6. ⎩⎨⎧x′+x+y=5e2ty′−5x−y=−3e2tx(0)=3y(0)=2

(7) given that taking Laplace transform both side putting value of x(0)=2 y(0)=1 __________(1) ...

Resuelto 5.5 Exercises Use the Laplace transform to solve each

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Pregunta: 5.5 Exercises Use the Laplace transform to solve each of the following systems of equations. 1. ⎩⎨⎧x′+y=3e2ty′+x=0x(0)=2y(0)=0 2. ⎩⎨⎧x′−2y=0y′+x−3y=2x(0)=3y(0)=0 3. ⎩⎨⎧x′−5x+2y=3e4ty′−4x+y=0x(0)=3y(0)=0 4. ⎩⎨⎧x′−2x−3y=0y′+x+2y=tx(0)=−1y(0)=0 5. ⎩⎨⎧x′−4x+2y=2ty′−8x+4y=1x(0)=3y(0)=5 6. ⎩⎨⎧x′+x+y=5e2ty′−5x−y=−3e2tx(0)=3y(0)=2
Can you do #7 please
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Solución
Paso 1
(7) given that
$2 x^{'} + y^{'} - x - y = e^{- t}$
taking Laplace transform both side
$L (2 x^{'} + y^{'} - x - y) = L (e^{- t})$
$2 s x (s) - 2 x (0) + s y (s) - y (0) - x (s) - y (s) = \frac{1}{s + 1}$
putting value of x(0)=2
y(0)=1
$(2 s - 1) x (s) - 4 - 1 + (s - 1) y (s) = \frac{1}{s + 1}$
$(2 s - 1) x (s) + (s - 1) y (s) = \frac{1}{s + 1} + 5$ __________(1)

$x^{'} + y^{'} + 2 x + y = e^{t}$ .
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Paso 2
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