laplacetransform t*e^{,\at}

解答

拉普拉斯变换

t \cdot e^{, at}

e^{, at} \frac{1}{s ^{2}}

求解步骤

L {e^{, at} t}

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)}

= e^{, at} L {t}

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

= e^{, at} \frac{1}{s ^{2}}

y^{^{'}} - 2 y = 4 e^{4 t}

\frac{\partial}{\partial x} (ln (x z) + y ln (x) - x^{2} + 4)

\int x (3 x - 2)^{2} d x

d er i v a t i v e f (x) = \frac{x ^{2} + 3 x}{6}

\int (6 x^{6} - 6 x^{5} - 4 x^{3} + 2) d x