Practice 4 Solutions

1 2 2 0 00 002 110 1 1 0 2t 1 e 1 te2t 0 1 y 2 2 0 2

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Unformatted text preview: e + te 0 6+ −2 y= 4 4 2 4 0 0 3t [3] Solve the di erential equation y = Ay where 211 A = 0 2 1 , 212 eAt 2 y ( 0) = 0 1 333 6 −3 −3 0 0 0 t t e e te 2 2 2 + −2 7 −2 + −2 1 1 = 9 9 3 444 −4 −4 5 2 −1 −1 4t λ = 4, 1, 1 9 9 0 t t e e te 6 + −6 + −3 y= 9 9 3 12 −3 3 4t , 3 × 3 Exercise Set F (repeated roots), November [4] Solve the di erential equation y = Ay where 111 A = 2 1 1 , 011 0 y ( 0) = 1 1 333 6 −3 −3 0 0 0 1 t e 4 4 4 + −4 5 −4 + 2 −1 −1 = 9 9 3 222 −2 −2 7 −2 1 1 3t λ = 3, 0, 0 eAt 6 −6 0 e 1 t 8 + 1 + −2 y= 9 9 3 4 5 2 3t [5] Solve the di erential equation y = Ay where 211 A = 1 2 0 , 222 λ = 4, 1, 1 eAt 0 y ( 0) = 1 2 442 5 −4 −2 −1 −1 1 et tet e4t 2 2 1 + −2 7 −1 + 1 1 −1 = 9 9 3 663 −6 −6 6 0 0 0 8 −8 1 t t e e te 4 + 5 + −1 y= 9 9 3 12 6 0 4t [6] Solve the di erential equation y = Ay where 100 A = 1 2 1 , 212 eAt 1 y ( 0) = 1 1 000 4 0 0 000 t t e te e 3 2 2 + −3 2 −2 + −1 0 0 = 4 4 2 322 −3 −2 2 100 3t λ = 3, 1, 1 0 4 0 t t e te e 7+ −3 + −1 y= 4 4 2 7 −3 1 3t [7] Solve the di erential equation y = Ay where 110 A = 1 1 0 , 112 1 y ( 0) = 0 1 , 3 × 3 Exercise Set F (repeated roots), November λ = 0, 2, 2 eAt 1 −1 0 110 000 2t 1 e 1 0 + 1 1 0 + te2t 0 0 0 = −1 2 2 0 00 002 110 1 1 0 2t 1 + e 1 + te2t 0 −1 y= 2 2 0 2 1 [8] Solve the di erential equation y = Ay where 111 A = 1 1 1 , 021 eAt 0 y ( 0) = 1 1 243 7 −4 −3 1 −1 0 1 t e 2 4 3 + −2 5 −3 + 1 −1...
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