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

Lösung

laplace transformation

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

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

Schritte zur Lösung

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

Verwende die konstante Multiplikationseigenschaft der Laplace-Transformation:

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}}

Fasse

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

zusammen:

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

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

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