What is laplacetransform e^{2t}sin(5t) ?

The answer to laplacetransform e^{2t}sin(5t) is 5/((s-2)^2+25)

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laplacetransform e^{2t}sin(5t)

laplace transform

e^{2 t} sin (5 t)

\frac{5}{( s - 2 ) ^{2} + 25}

Solution steps

L {e^{2 t} sin (5 t)}

Apply transform rule:

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

then

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

For

e^{2 t} sin (5 t) : f (t) = sin (5 t), a = 2

= L {sin (5 t)} (s - 2)

L {sin (5 t)} : \frac{5}{s ^{2} + 25}

= \frac{5}{( s - 2 ) ^{2} + 25}

What is laplacetransform e^{2t}sin(5t) ?
The answer to laplacetransform e^{2t}sin(5t) is 5/((s-2)^2+25)