Question

4- Use the Laplace Transform method to solve the following IVP. Where [ egin{array}{c} y^{prime prime}+4 y^{prime}+4 y=g(t), y(0)=3, y^{prime}(0)=-2 \ g(t)=left{egin{array}{ll} e^{2 t} & ext { if } 0 leq t<2 \ e^{2 t}-1 & ext { if } 2 leq t end{array} ight} end{array} ]

          4- Use the Laplace Transform method to solve the following IVP.
Where
[
egin{array}{c}
y^{prime prime}+4 y^{prime}+4 y=g(t), y(0)=3, y^{prime}(0)=-2 \
g(t)=left{egin{array}{ll}
e^{2 t} & 	ext { if } 0 leq t<2 \
e^{2 t}-1 & 	ext { if } 2 leq t
end{array}
ight}
end{array}
]

4- Use the Laplace Transform method to solve the following IVP.
Where
[
eginarrayc
y^prime prime+4 y^prime+4 y=g(t), y(0)=3, y^prime(0)=-2 g(t)=lefteginarrayll
e^2 t ext if 0 leq t<2 e^2 t-1 ext if 2 leq t
endarray
ight
endarray
]

Added by Jose

Advanced Engineering Mathematics

Dennis G. Zill, Warren S. Wright 5th Edition

Chapter 4

Instant Answer

Solved by Expert Sam Stansfield

04/13/2024

Step 1

Recall that the Laplace Transform of \(y(t)\) is denoted as \(L\{y(t)\} = Y(s)\), and we use the properties of Laplace Transforms for derivatives, which are \(L\{y'\} = sY(s) - y(0)\) and \(L\{y''\} = s^2Y(s) - sy(0) - y'(0)\). Show more…

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