What is laplacetransform 3e^{-4t}-5e^{4t} ?

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

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laplacetransform 3e^{-4t}-5e^{4t}

laplace transform

3 e^{- 4 t} - 5 e^{4 t}

\frac{3}{s + 4} - \frac{5}{s - 4}

Solution steps

L {3 e^{- 4 t} - 5 e^{4 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^{- 4 t}} - 5 L {e^{4 t}}

L {e^{- 4 t}} : \frac{1}{s + 4}

L {e^{4 t}} : \frac{1}{s - 4}

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

Refine

3 \frac{1}{s + 4} - 5 \frac{1}{s - 4} : \frac{3}{s + 4} - \frac{5}{s - 4}

= \frac{3}{s + 4} - \frac{5}{s - 4}

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

\int tan^{2} (x + c) + 1 d x

x^{2}, 1

y^{^{''''}} + y^{^{''}} = 0

\frac{\partial}{\partial x} (x z - e^{x} sin (y))

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