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人気のある微分積分 >

laplacetransform e^{2t}sin(4t)

解

ラプラス変換

e^{2 t} sin (4 t)

解

\frac{4}{( s - 2 ) ^{2} + 16}

解答ステップ

L {e^{2 t} sin (4 t)}

変換ルールを適用:

L {f (t)} = F (s)

ならば

L {e^{a t} f (t)} = F (s - a)

e^{2 t} sin (4 t)

向け

: f (t) = sin (4 t), a = 2

= L {sin (4 t)} (s - 2)

L {sin (4 t)} : \frac{4}{s ^{2} + 16}

= \frac{4}{( s - 2 ) ^{2} + 16}

人気の例

derivative (x^3-2)^2

d er i v a t i v e (x^{3} - 2)^{2}

derivative of sqrt(x)-6x

\frac{d}{d x} (x - 6 x)

limit as x approaches 1 of x^3

x \to 1 lim (x^{3})

limit as x approaches+3 of 5/(x^2-9)

x \to + 3 lim (\frac{5}{x ^{2} - 9})

(dy)/(dt)=20-y/(230+16t)

\frac{d y}{d t} = 20 - \frac{y}{230 + 16 t}