What is laplacetransform 2e^{3t}sin(4t) ?

The answer to laplacetransform 2e^{3t}sin(4t) is 8/((s-3)^2+16)

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laplacetransform 2e^{3t}sin(4t)

laplace transform

2 e^{3 t} sin (4 t)

\frac{8}{( s - 3 ) ^{2} + 16}

Solution steps

L {2 e^{3 t} sin (4 t)}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= 2 L {e^{3 t} sin (4 t)}

L {e^{3 t} sin (4 t)} : \frac{4}{( s - 3 ) ^{2} + 16}

= 2 \cdot \frac{4}{( s - 3 ) ^{2} + 16}

Refine

2 \frac{4}{( s - 3 ) ^{2} + 16} : \frac{8}{( s - 3 ) ^{2} + 16}

= \frac{8}{( s - 3 ) ^{2} + 16}

\frac{d}{d x} (ln (x) csch (7 x))

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

\int sin (x) + y d x

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

\int x^{7} arctan (x^{4}) d x

What is laplacetransform 2e^{3t}sin(4t) ?
The answer to laplacetransform 2e^{3t}sin(4t) is 8/((s-3)^2+16)