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

The answer to inverse oflaplace ((s+3))/((s-2)^2) is e^{2t}+e^{2t}*5t

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

inverse laplace

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

e^{2 t} + e^{2 t} \cdot 5 t

Solution steps

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

Take the partial fraction of

\frac{s + 3}{( s - 2 ) ^{2}} : \frac{1}{s - 2} + \frac{5}{( s - 2 ) ^{2}}

= L^{- 1} {\frac{1}{s - 2} + \frac{5}{( s - 2 ) ^{2}}}

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)}

= L^{- 1} {\frac{1}{s - 2}} + L^{- 1} {\frac{5}{( s - 2 ) ^{2}}}

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

L^{- 1} {\frac{5}{( s - 2 ) ^{2}}} : e^{2 t} \cdot 5 t

= e^{2 t} + e^{2 t} \cdot 5 t

x \to 6 lim (x)

f (x) = x^{3} - x, [0, 3]

\int sin (x - 2 n x) d x

\frac{d}{d x} (x^{5} y^{2})

\int \frac{1}{( x - 1 ) ^{\frac{3}{2}}} d x

What is inverse oflaplace ((s+3))/((s-2)^2) ?
The answer to inverse oflaplace ((s+3))/((s-2)^2) is e^{2t}+e^{2t}*5t