If * represents convolution, determine the Laplace transform of f(t) = 12t * e-3t

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Q: Determine the solution of the following differential equations. a) (D² +9) y = 81x² + 14cos3x

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Q: = (-² −4) ² (a) AB If A = -6-16 (c) 14+24 (b) BA -6-63 12-21 A² = AA 9+28 -21-42 and B = =(-²3). 4…

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Q: 12 Let u₁ = 1, ₂ = 1 and un + 2 = Un + 1 + un n ≥ 1. Then use mathematical induction to show that 1…

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Q: Problem A £2 points). Complete the definition of an equivalence relation by filling in the two…

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Q: 6. Consider the vector field defined by y F = (²) ² + ( 3y² m (x) - ₂ √ √ ) ³ + ( √T)k i j (a) Use…

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Q: (b) For ($(t) = (ýdı yöu). let y^² = 4²" + c₂us →di y" (0) = (6) >> So you = ( 2 Sintl) + (os (t)…

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Q: 6. y4y' + 5y = 4e³; y(0) = 2, y' (0) = 7

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