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

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

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laplacetransform e^{2t}sin(3t)

laplace transform

e^{2 t} sin (3 t)

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

Solution steps

L {e^{2 t} sin (3 t)}

Apply transform rule:

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

then

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

For

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

= L {sin (3 t)} (s - 2)

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

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

y = 3 x, y = 9, y = \frac{1}{4} x^{2}

\int (x^{3} + 2)^{8} 3 x^{2} d x

\frac{d}{d x} (5 x - x)

x \to - \frac{π}{2} lim (csc (x))

ln (4 x - x^{2} - 3)

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