What is laplacetransform (7-e^{(-t)/5})/(6) ?

The answer to laplacetransform (7-e^{(-t)/5})/(6) is 7/(6s)-5/(6(5s+1))

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laplacetransform (7-e^{(-t)/5})/(6)

laplace transform

\frac{7 - e ^{\frac{- t}{5}}}{6}

\frac{7}{6 s} - \frac{5}{6 ( 5 s + 1 )}

Solution steps

L {\frac{7 - e ^{\frac{- t}{5}}}{6}}

Expand

= L {- \frac{e ^{\frac{- t}{5}}}{6} + \frac{7}{6}}

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 {\frac{7}{6}} - \frac{1}{6} L {e^{\frac{- 1}{5} t}}

L {\frac{7}{6}} : \frac{7}{6 s}

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

= \frac{7}{6 s} - \frac{1}{6} \cdot \frac{5}{5 s + 1}

Refine

\frac{7}{6 s} - \frac{1}{6} \frac{5}{5 s + 1} : \frac{7}{6 s} - \frac{5}{6 ( 5 s + 1 )}

= \frac{7}{6 s} - \frac{5}{6 ( 5 s + 1 )}

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

y^{^{''}} + 12 y^{^{'}} + 36 y = e - 7 x (x^{2} + 3 x + 6)

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

n = 0 \sum \infty x (2 x)^{n}

f (x) = x x, at x = 1

What is laplacetransform (7-e^{(-t)/5})/(6) ?
The answer to laplacetransform (7-e^{(-t)/5})/(6) is 7/(6s)-5/(6(5s+1))