What is laplacetransform 3-sin(2t)+e^{5t} ?

The answer to laplacetransform 3-sin(2t)+e^{5t} is 3/s-2/(s^2+4)+1/(s-5)

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laplacetransform 3-sin(2t)+e^{5t}

laplace transform

3 - sin (2 t) + e^{5 t}

\frac{3}{s} - \frac{2}{s ^{2} + 4} + \frac{1}{s - 5}

Solution steps

L {3 - sin (2 t) + e^{5 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)}

= L {3} - L {sin (2 t)} + L {e^{5 t}}

L {3} : \frac{3}{s}

L {sin (2 t)} : \frac{2}{s ^{2} + 4}

L {e^{5 t}} : \frac{1}{s - 5}

= \frac{3}{s} - \frac{2}{s ^{2} + 4} + \frac{1}{s - 5}

38 (2 e^{x^{2}} x^{2} + e^{x^{2}})

\frac{d y}{d x} = sin (x^{2})

\frac{d}{d x} ((2 + 1) e^{2 x})

\int \frac{e ^{x - 1 + l n (x - 1)}}{e ^{2 x}} d x

\int (\frac{15}{x ^{2} + 1}) d x

What is laplacetransform 3-sin(2t)+e^{5t} ?
The answer to laplacetransform 3-sin(2t)+e^{5t} is 3/s-2/(s^2+4)+1/(s-5)