What is laplacetransform e^{-2t}cos(3t) ?

The answer to laplacetransform e^{-2t}cos(3t) is (s+2)/((s+2)^2+9)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

laplacetransform e^{-2t}cos(3t)

laplace transform

e^{- 2 t} cos (3 t)

\frac{s + 2}{( s + 2 ) ^{2} + 9}

Solution steps

L {e^{- 2 t} cos (3 t)}

Apply transform rule:

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

then

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

For

e^{- 2 t} cos (3 t) : f (t) = cos (3 t), a = - 2

= L {cos (3 t)} (s + 2)

L {cos (3 t)} : \frac{s}{s ^{2} + 9}

= \frac{( s + 2 )}{( s + 2 ) ^{2} + 9}

= \frac{s + 2}{( s + 2 ) ^{2} + 9}

\frac{\partial}{\partial y} (y + 1)

\frac{6}{( s + 1 ) ( 2 s ^{2} + 5 s + 3 )}

\int_{0}^{1} \frac{x ^{2}}{( x + 3 ) ^{2}} d x

\int e^{10 x} \cdot 5 x d x

x = 4 y, x = y^{2} - 5

What is laplacetransform e^{-2t}cos(3t) ?
The answer to laplacetransform e^{-2t}cos(3t) is (s+2)/((s+2)^2+9)