laplacetransform te^{6t}sin(3t)

Lösung

laplace transformation

t e^{6 t} sin (3 t)

\frac{3 ( 2 s - 12 )}{( s ^{2} - 12 s + 45 ) ^{2}}

Schritte zur Lösung

L {e^{6 t} t sin (3 t)}

Wende Laplace-Transformationstabelle an:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

Für

t e^{6 t} sin (3 t) : f (t) = e^{6 t} sin (3 t), k = 1

= (- 1)^{1} \frac{d}{d s} (L {e^{6 t} sin (3 t)})

L {e^{6 t} sin (3 t)} : \frac{3}{( s - 6 ) ^{2} + 9}

\frac{d}{d s} (\frac{3}{( s - 6 ) ^{2} + 9}) = - \frac{3 ( 2 s - 12 )}{( s ^{2} - 12 s + 45 ) ^{2}}

= (- 1)^{1} (- \frac{3 ( 2 s - 12 )}{( s ^{2} - 12 s + 45 ) ^{2}})

= \frac{3 ( 2 s - 12 )}{( s ^{2} - 12 s + 45 ) ^{2}}

l a pl a ce t r an s f or m e^{t} \cdot cos (t)

(5 y - 2 x) (\frac{d y}{d x}) - 2 y = 0

s l o p e in t erce pt (5) (0.5)

a re a y = x^{2} - 7, y = 2

x \to 2 lim (- x^{3} + 2 x^{2} - 1)