What is inverse oflaplace (2s+3)/(s^2+17) ?

The answer to inverse oflaplace (2s+3)/(s^2+17) is 2cos(sqrt(17)t)+3/(sqrt(17))sin(sqrt(17)t)

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inverse oflaplace (2s+3)/(s^2+17)

inverse laplace

\frac{2 s + 3}{s ^{2} + 17}

2 cos (17 t) + \frac{3}{17} sin (17 t)

Solution steps

L^{- 1} {\frac{2 s + 3}{s ^{2} + 17}}

Expand

= L^{- 1} {\frac{2 s}{s ^{2} + 17} + \frac{3}{s ^{2} + 17}}

Use the linearity property of Inverse Laplace Transform:

For functions

f (s), g (s)

and constants

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

= 2 L^{- 1} {\frac{s}{s ^{2} + 17}} + 3 L^{- 1} {\frac{1}{s ^{2} + 17}}

L^{- 1} {\frac{s}{s ^{2} + 17}} : cos (17 t)

L^{- 1} {\frac{1}{s ^{2} + 17}} : \frac{1}{17} sin (17 t)

= 2 cos (17 t) + 3 \cdot \frac{1}{17} sin (17 t)

Refine

2 cos (17 t) + 3 \frac{1}{17} sin (17 t) : 2 cos (17 t) + \frac{3}{17} sin (17 t)

= 2 cos (17 t) + \frac{3}{17} sin (17 t)

\int x + 1 + \frac{2}{3} x d x

x \to + 0 + lim (\frac{2}{1 + ln ( x )})

y = 4 x - x^{2}

\int 20 t (5 t^{2} - 3)^{3} d t

n = 5 \sum \infty \frac{1}{n ln ( n )}

What is inverse oflaplace (2s+3)/(s^2+17) ?
The answer to inverse oflaplace (2s+3)/(s^2+17) is 2cos(sqrt(17)t)+3/(sqrt(17))sin(sqrt(17)t)