What is laplacetransform {e^tsin(3t)} ?

The answer to laplacetransform {e^tsin(3t)} is 3/((s-1)^2+9)

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laplacetransform {e^tsin(3t)}

laplace transform

{e^{t} sin (3 t)}

\frac{3}{( s - 1 ) ^{2} + 9}

Solution steps

L {e^{t} sin (3 t)}

Apply transform rule:

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

then

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

For

e^{t} sin (3 t) : f (t) = sin (3 t), a = 1

= L {sin (3 t)} (s - 1)

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

= \frac{3}{( s - 1 ) ^{2} + 9}

n = 1 \sum \infty \frac{ln ( 6 n )}{n}

\frac{\frac{1}{2}}{s ^{2} + 2 s + 3}

3 (3 x^{2} + y^{2}) d x - 2 x y d y = 0

t + y e^{2 t y} + t e^{2 t y} \frac{d y}{d t} = 0

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

What is laplacetransform {e^tsin(3t)} ?
The answer to laplacetransform {e^tsin(3t)} is 3/((s-1)^2+9)