What is laplacetransform f(t)= 1/20 t^5e^{2t} ?

The answer to laplacetransform f(t)= 1/20 t^5e^{2t} is 6/((s-2)^6)

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laplacetransform f(t)= 1/20 t^5e^{2t}

laplace transform

f (t) = \frac{1}{20} t^{5} e^{2 t}

\frac{6}{( s - 2 ) ^{6}}

Solution steps

L {\frac{1}{20} e^{2 t} t^{5}}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= \frac{1}{20} L {t^{5} e^{2 t}}

L {t^{5} e^{2 t}} : \frac{120}{( s - 2 ) ^{6}}

= \frac{1}{20} \cdot \frac{120}{( s - 2 ) ^{6}}

Refine

\frac{1}{20} \frac{120}{( s - 2 ) ^{6}} : \frac{6}{( s - 2 ) ^{6}}

= \frac{6}{( s - 2 ) ^{6}}

x \to 0 lim ((x)^{2})

\int \frac{1}{6 x ^{2} + 36 x + 78} d x

tan (x) sin (y) d x + cos (x) cot (y) d y = 0

\int \frac{2 x ^{2} - x + 4}{x ( x ^{2} + 4 )} d x

y^{^{''}} - 2 y^{^{'}} + y = t e^{t}, y (0) = 1, y^{^{'}} (0) = 1

What is laplacetransform f(t)= 1/20 t^5e^{2t} ?
The answer to laplacetransform f(t)= 1/20 t^5e^{2t} is 6/((s-2)^6)