laplacetransform (et^4)/(24)

解答

拉普拉斯变换

\frac{e t ^{4}}{24}

\frac{e}{s ^{5}}

求解步骤

L {\frac{e t ^{4}}{24}}

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)}

= \frac{e}{24} L {t^{4}}

L {t^{4}} : \frac{24}{s ^{5}}

= \frac{e}{24} \cdot \frac{24}{s ^{5}}

整理

\frac{e}{24} \frac{24}{s ^{5}} : \frac{e}{s ^{5}}

= \frac{e}{s ^{5}}

\frac{d x}{d t} + x e^{t} = 1 - x

s l o p e (5, - 6), (8, - 4)

x \to 0 lim (1 - 3 x)

x y^{^{'}} + \frac{1}{2} y = x

\frac{\partial}{\partial x} (ln (x^{4} y))