laplacetransform x^2cos(x)

解

ラプラス変換

x^{2} cos (x)

- \frac{2 s ( - s ^{2} + 3 )}{( s ^{2} + 1 ) ^{3}}

解答ステップ

L {x^{2} cos (x)}

ラプラス変換表を使用する:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

x^{2} cos (x)

向け

: f (x) = cos (x), k = 2

= (- 1)^{2} \frac{d ^{2}}{d s ^{2}} (L {cos (x)})

L {cos (x)} : \frac{s}{s ^{2} + 1}

\frac{d ^{2}}{d s ^{2}} (\frac{s}{s ^{2} + 1}) = - \frac{2 s ( - s ^{2} + 3 )}{( s ^{2} + 1 ) ^{3}}

= (- 1)^{2} (- \frac{2 s ( - s ^{2} + 3 )}{( s ^{2} + 1 ) ^{3}})

= - \frac{2 s ( - s ^{2} + 3 )}{( s ^{2} + 1 ) ^{3}}