laplacetransform t^2e^{,\at}

解答

拉普拉斯变换

t^{2} e^{, at}

e^{, at} \frac{2}{s ^{3}}

求解步骤

L {e^{, at} 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)}

= e^{, at} L {t^{2}}

L {t^{2}} : \frac{2}{s ^{3}}

= e^{, at} \frac{2}{s ^{3}}

\frac{\partial}{\partial x} (3 x^{3} + 4 x^{2} y - 4 y^{3})

\frac{d}{d x} (5 ln (sec (x) + tan (x)))

\int \frac{( arctan ( x ) ) ^{2}}{1 + x ^{2}} d x

y y^{^{'}} + x y^{2} = (e^{- x^{2}})

t an g e n t f (x) = \frac{1}{3} x^{3} + 5.5 x^{2} + 30 x + 22