laplacetransform 2(s+2)

解答

拉普拉斯变换

2 (s + 2)

\frac{2}{s ^{2}} + \frac{4}{s}

求解步骤

L {2 (s + 2)}

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2 (s + 2) : 2 s + 4

= L {2 s + 4}

利用拉普拉斯变换的线性特性:

对于函数

f (t), g (t)

和常数

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= 2 L {s} + L {4}

L {s} : \frac{1}{s ^{2}}

L {4} : \frac{4}{s}

= 2 \cdot \frac{1}{s ^{2}} + \frac{4}{s}

整理

2 \frac{1}{s ^{2}} + \frac{4}{s} : \frac{2}{s ^{2}} + \frac{4}{s}

= \frac{2}{s ^{2}} + \frac{4}{s}

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t a y l or \frac{1}{x + 1}

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y^{^{''}} + 8 y^{^{'}} = - 256 cos (8 x)