展开 (5t+e^{-2t}cos(7t))u(t)

解答

展开

(5 t + e^{- 2 t} cos (7 t)) u (t)

5 t^{2} u + e^{- 2 t} t u cos (7 t)

求解步骤

(5 t + e^{- 2 t} cos (7 t)) u (t)

= (t) u (5 t + e^{- 2 t} cos (7 t))

使用分配律:

a (b + c) = ab + a c

a = u (t), b = 5 t, c = e^{- 2 t} cos (7 t)

= u (t) \cdot 5 t + u (t) e^{- 2 t} cos (7 t)

= 5 (t) t u + e^{- 2 t} (t) u cos (7 t)

化简

5 (t) t u + e^{- 2 t} (t) u cos (7 t) : 5 t^{2} u + e^{- 2 t} t u cos (7 t)

= 5 t^{2} u + e^{- 2 t} t u cos (7 t)

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