What is laplacetransform f(t)= 9/4 t^2*e^{2t}*e^{3t} ?

The answer to laplacetransform f(t)= 9/4 t^2*e^{2t}*e^{3t} is 9/(2(s-5)^3)

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laplacetransform f(t)= 9/4 t^2e^{2t}e^{3t}

laplace transform

f (t) = \frac{9}{4} t^{2} \cdot e^{2 t} \cdot e^{3 t}

\frac{9}{2 ( s - 5 ) ^{3}}

Solution steps

L {\frac{9}{4} e^{2 t} e^{3 t} t^{2}}

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{9}{4} L {t^{2} e^{2 t} e^{3 t}}

L {t^{2} e^{2 t} e^{3 t}} : \frac{2}{( s - 5 ) ^{3}}

= \frac{9}{4} \cdot \frac{2}{( s - 5 ) ^{3}}

Refine

\frac{9}{4} \frac{2}{( s - 5 ) ^{3}} : \frac{9}{2 ( s - 5 ) ^{3}}

= \frac{9}{2 ( s - 5 ) ^{3}}

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What is laplacetransform f(t)= 9/4 t^2*e^{2t}*e^{3t} ?
The answer to laplacetransform f(t)= 9/4 t^2*e^{2t}*e^{3t} is 9/(2(s-5)^3)