What is laplacetransform 3t^2-5e^{3t} ?

The answer to laplacetransform 3t^2-5e^{3t} is 6/(s^3)-5/(s-3)

Popular >

laplacetransform 3t^2-5e^{3t}

laplace transform

3 t^{2} - 5 e^{3 t}

\frac{6}{s ^{3}} - \frac{5}{s - 3}

Solution steps

L {3 t^{2} - 5 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}} - 5 L {e^{3 t}}

L {t^{2}} : \frac{2}{s ^{3}}

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

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

Refine

3 \frac{2}{s ^{3}} - 5 \frac{1}{s - 3} : \frac{6}{s ^{3}} - \frac{5}{s - 3}

= \frac{6}{s ^{3}} - \frac{5}{s - 3}

x \to 2 a lim (\frac{x ^{2} - 2 a x + a ^{2}}{x ^{3} - a ^{3}})

\int_{2}^{4} 3 x d x

\frac{\partial}{\partial x} (arctan (2 x))

x \to - 1 lim (- 1 (x + 1))

\frac{d}{d x} (7 x + 3)

What is laplacetransform 3t^2-5e^{3t} ?
The answer to laplacetransform 3t^2-5e^{3t} is 6/(s^3)-5/(s-3)