laplacetransform e^{(3t)}(4cos(3t)-10/3 sin(3t))

Lösung

laplace transformation

e^{(3 t)} (4 cos (3 t) - \frac{10}{3} sin (3 t))

\frac{4 ( s - 3 )}{( s - 3 ) ^{2} + 9} - \frac{10}{( s - 3 ) ^{2} + 9}

Schritte zur Lösung

L {e^{(3 t)} (4 cos (3 t) - \frac{10}{3} sin (3 t))}

Wende Transformationsregel an: wenn

L {f (t)} = F (s)

dann

L {e^{a t} f (t)} = F (s - a)

Für

e^{3 t} (4 cos (3 t) - \frac{10}{3} sin (3 t)) : f (t) = (4 cos (3 t) - \frac{10}{3} sin (3 t)), a = 3

= L {(4 cos (3 t) - \frac{10}{3} sin (3 t))} (s - 3)

L {(4 cos (3 t) - \frac{10}{3} sin (3 t))} : \frac{4 s}{s ^{2} + 9} - \frac{10}{s ^{2} + 9}

= \frac{4 ( s - 3 )}{( s - 3 ) ^{2} + 9} - \frac{10}{( s - 3 ) ^{2} + 9}

x \to - 1 + lim (\frac{x}{∣ x + 1 ∣})

so l v e f or y, y = x e^{y}

\int_{- 3}^{- 2} (2 x (3 - x^{2})^{3}) d x

t an g e n t f (x) = cos (x), at x = π

in v erse l a pl a ce \frac{e ^{- 4 s}}{s ( s ^{2} + 16 )}