What is laplacetransform 3t+2e^{3t} ?

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

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laplacetransform 3t+2e^{3t}

laplace transform

3 t + 2 e^{3 t}

\frac{3}{s ^{2}} + \frac{2}{s - 3}

Solution steps

L {3 t + 2 e^{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 {t} + 2 L {e^{3 t}}

L {t} : \frac{1}{s ^{2}}

L {e^{3 t}} : \frac{1}{s - 3}

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

Refine

3 \frac{1}{s ^{2}} + 2 \frac{1}{s - 3} : \frac{3}{s ^{2}} + \frac{2}{s - 3}

= \frac{3}{s ^{2}} + \frac{2}{s - 3}

\frac{\partial}{\partial x} ((sin (y)) u (x, π))

\int_{0}^{\frac{3}{2}} \frac{1}{36 + 16 x ^{2}} d x

\frac{1}{( 16 x ^{2} )}, x, \frac{x}{6}

j = 0 \sum \infty \frac{7}{5 ^{j}}

\frac{d}{d x} (\frac{x}{cos ( x )})

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