laplacetransform 2e^{t/2}

解答

拉普拉斯变换

2 e^{\frac{t}{2}}

\frac{4}{2 s - 1}

求解步骤

L {2 e^{\frac{t}{2}}}

利用拉普拉斯变换的常数乘法特性:

对于函数

f (t)

和常数

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= 2 L {e^{\frac{1}{2} t}}

L {e^{\frac{1}{2} t}} : \frac{2}{2 s - 1}

= 2 \cdot \frac{2}{2 s - 1}

整理

2 \frac{2}{2 s - 1} : \frac{4}{2 s - 1}

= \frac{4}{2 s - 1}

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