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Beliebt Rechnen >

laplacetransform F(x)=e^{2x}cos(2x)

Lösung

laplace transformation

F (x) = e^{2 x} cos (2 x)

Lösung

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

Schritte zur Lösung

L {e^{2 x} cos (2 x)}

Wende Transformationsregel an: wenn

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

dann

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

Für

e^{2 x} cos (2 x) : f (x) = cos (2 x), a = 2

= L {cos (2 x)} (s - 2)

L {cos (2 x)} : \frac{s}{s ^{2} + 4}

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

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

Beliebte Beispiele

integral of (2x^2)/3

\int \frac{2 x ^{2}}{3} d x

integral of sin(12x)\sqrt[3]{cos(12x)}

\int sin (12 x) 3 cos (12 x) d x

integral of 5xe^{3x^2}

\int 5 x e^{3 x^{2}} d x

integral of 7sin(x)cos(x)

\int 7 sin (x) cos (x) d x

d/(dt)((csc^2(t))/(-cot(t)(csc(t))))

\frac{d}{d t} (\frac{csc ^{2} ( t )}{- cot ( t ) ( csc ( t ) )})