展开 (e^{-3t}+e^{-2t})u(t)

解答

展开

(e^{- 3 t} + e^{- 2 t}) u (t)

e^{- 3 t} t u + e^{- 2 t} t u

求解步骤

(e^{- 3 t} + e^{- 2 t}) u (t)

= (t) u (e^{- 3 t} + e^{- 2 t})

使用分配律:

a (b + c) = ab + a c

a = u (t), b = e^{- 3 t}, c = e^{- 2 t}

= u (t) e^{- 3 t} + u (t) e^{- 2 t}

= e^{- 3 t} (t) u + e^{- 2 t} (t) u

去除括号:

(a) = a

= e^{- 3 t} t u + e^{- 2 t} t u

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