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FIND THE GENERAL SOLUTION TO THE DE: Yâ€â€™ + 4Yâ€ â€“ Yâ€™ â€“ 4Y = 0 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â COMPUTE:Â Â Â Â Â Â Â Â Â Â Â Â Â Â L...

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FIND THE GENERAL SOLUTION TO THE DE: Yâ€â€™ + 4Yâ€ â€“ Yâ€™ â€“4Y = 0
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
COMPUTE:Â Â Â Â Â Â Â Â Â Â Â Â Â Â L {7 e ^3t â€“ 5 cos ( 2t ) â€“ 4 t ²}Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
COMPUTE:Â Â Â Â Â Â Â Â Â Â Â Â Â L ^{â€“ 1} {(3s + 6 ) / [ s ( s ² + s â€“ 6 ) ]}Â Â Â Â Â Â Â Â Â Â Â
SOLVE THE INITIAL VALUE PROBLEM USING LAPLACETRANSFORMS:Â Â Â Â Â Â Â Â Â Â Â Â Â
Yâ€ + 6Yâ€™ + 5Y = 12 e ^tÂ Â Â Â Â Â WHEN :Â Â f ( 0 ) = -1, AND f â€˜ ( 0 ) =7.Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
SOLVE THE SYSTEM USING LAPLACETRANSFORMS:Â Â Â Xâ€™ â€“ X â€“ Y = 1,Â Â Â AND:Â Â â€“ X + Yâ€™ â€“ Y = 0, WHEN:Â Â X = f ( 0 ) = 0,AND: Y = g ( 0 ) = - ( 5 / 2) Â Â

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