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

The answer to laplacetransform 3*e^{-2t}+2*sin(3t) is 3/(s+2)+6/(s^2+9)

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

laplace transform

3 \cdot e^{- 2 t} + 2 \cdot sin (3 t)

\frac{3}{s + 2} + \frac{6}{s ^{2} + 9}

Solution steps

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

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

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

L {e^{- 2 t}} : \frac{1}{s + 2}

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

= 3 \cdot \frac{1}{s + 2} + 2 \cdot \frac{3}{s ^{2} + 9}

Refine

3 \frac{1}{s + 2} + 2 \frac{3}{s ^{2} + 9} : \frac{3}{s + 2} + \frac{6}{s ^{2} + 9}

= \frac{3}{s + 2} + \frac{6}{s ^{2} + 9}

What is laplacetransform 3*e^{-2t}+2*sin(3t) ?
The answer to laplacetransform 3*e^{-2t}+2*sin(3t) is 3/(s+2)+6/(s^2+9)